OP-AMPLIFIERS

Operational Amplifier Basics

As well as resistors and capacitors, Operational Amplifiers, or Op-amps as they are more commonly called, are one of the basic building blocks of Analogue Electronic Circuits.

                             

                          

                             Operational amplifiers are linear devices that have all the properties required for nearly ideal DC amplification and are therefore used extensively in signal conditioning, filtering or to perform mathematical operations such as add, subtract, integration and differentiation.

An Operational Amplifier, or op-amp for short, is fundamentally a voltage amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals. These feedback components determine the resulting function or “operation” of the amplifier and by virtue of the different feedback configurations whether resistive, capacitive or both, the amplifier can perform a variety of different operations, giving rise to its name of “Operational Amplifier”.

An Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs, one called the Inverting Input, marked with a negative or “minus” sign, ( – ) and the other one called the Non-inverting Input, marked with a positive or “plus” sign ( + ).

The third terminal represents the operational amplifiers output port which can both sink and source either a voltage or a current. In a linear operational amplifier, the output signal is the amplification factor, known as the amplifiers gain ( A ) multiplied by the value of the input signal and depending on the nature of these input and output signals, there can be four different classifications of operational amplifier gain.

• Voltage  – Voltage “in” and Voltage “out”
• Current  – Current “in” and Current “out”
• Transconductance  – Voltage “in” and Current “out”
• Transresistance  – Current “in” and Voltage “out”

Since most of the circuits dealing with operational amplifiers are voltage amplifiers, we will limit the tutorials in this section to voltage amplifiers only, (Vin and Vout).

The output voltage signal from an Operational Amplifier is the difference between the signals being applied to its two individual inputs. In other words, an op-amps output signal is the difference between the two input signals as the input stage of an Operational Amplifier is in fact a differential amplifier as shown below.

Differential Amplifier

The circuit below shows a generalized form of a differential amplifier with two inputs marked V1 and V2. The two identical transistors TR1 and TR2 are both biased at the same operating point with their emitters connected together and returned to the common rail, -Vee by way of resistor Re.

Differential Amplifier

The circuit operates from a dual supply +Vcc and -Vee which ensures a constant supply. The voltage that appears at the output, Vout of the amplifier is the difference between the two input signals as the two base inputs are in anti-phase with each other.

So as the forward bias of transistor, TR1 is increased, the forward bias of transistor TR2 is reduced and vice versa. Then if the two transistors are perfectly matched, the current flowing through the common emitter resistor, Re will remain constant.

Like the input signal, the output signal is also balanced and since the collector voltages either swing in opposite directions (anti-phase) or in the same direction (in-phase) the output voltage signal, taken from between the two collectors is, assuming a perfectly balanced circuit the zero difference between the two collector voltages.

This is known as the Common Mode of Operation with the common mode gain of the amplifier being the output gain when the input is zero.

Operational Amplifiers also have one output (although there are ones with an additional differential output) of low impedance that is referenced to a common ground terminal and it should ignore any common mode signals that is, if an identical signal is applied to both the inverting and non-inverting inputs there should no change to the output.

However, in real amplifiers there is always some variation and the ratio of the change to the output voltage with regards to the change in the common mode input voltage is called the Common Mode Rejection Ratio or CMRR for short.

Operational Amplifiers on their own have a very high open loop DC gain and by applying some form of Negative Feedback we can produce an operational amplifier circuit that has a very precise gain characteristic that is dependant only on the feedback used. Note that the term “open loop” means that there are no feedback components used around the amplifier so the feedback path or loop is open.

An operational amplifier only responds to the difference between the voltages on its two input terminals, known commonly as the “Differential Input Voltage” and not to their common potential. Then if the same voltage potential is applied to both terminals the resultant output will be zero. An Operational Amplifiers gain is commonly known as the Open Loop Differential Gain, and is given the symbol (Ao).

Equivalent Circuit of an Ideal Operational Amplifier

Op-amp Parameter and Idealised Characteristic

• Open Loop Gain, (Avo)

  • Infinite – The main function of an operational amplifier is to amplify the input signal and the more open loop gain it has the better. Open-loop gain is the gain of the op-amp without positive or negative feedback and for such an amplifier the gain will be infinite but typical real values range from about 20,000 to 200,000.

• Input impedance, (ZIN)

  • Infinite – Input impedance is the ratio of input voltage to input current and is assumed to be infinite to prevent any current flowing from the source supply into the amplifiers input circuitry ( IIN = 0 ). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps.

• Output impedance, (ZOUT)

  • Zero – The output impedance of the ideal operational amplifier is assumed to be zero acting as a perfect internal voltage source with no internal resistance so that it can supply as much current as necessary to the load. This internal resistance is effectively in series with the load thereby reducing the output voltage available to the load. Real op-amps have output impedances in the 100-20kΩ range.

• Bandwidth, (BW)

  • Infinite – An ideal operational amplifier has an infinite frequency response and can amplify any frequency signal from DC to the highest AC frequencies so it is therefore assumed to have an infinite bandwidth. With real op-amps, the bandwidth is limited by the Gain-Bandwidth product (GB), which is equal to the frequency where the amplifiers gain becomes unity.

• Offset Voltage, (VIO)

  • Zero – The amplifiers output will be zero when the voltage difference between the inverting and the non-inverting inputs is zero, the same or when both inputs are grounded. Real op-amps have some amount of output offset voltage.

From these “idealized” characteristics above, we can see that the input resistance is infinite, so no current flows into either input terminal (the “current rule”) and that the differential input offset voltage is zero (the “voltage rule”). It is important to remember these two properties as they will help us understand the workings of the Operational Amplifier with regards to the analysis and design of op-amp circuits.

However, real Operational Amplifiers such as the commonly available uA741, for example do not have infinite gain or bandwidth but have a typical “Open Loop Gain” which is defined as the amplifiers output amplification without any external feedback signals connected to it and for a typical operational amplifier is about 100dB at DC (zero Hz). This output gain decreases linearly with frequency down to “Unity Gain” or 1, at about 1MHz and this is shown in the following open loop gain response curve.

Open-loop Frequency Response Curve

From this frequency response curve we can see that the product of the gain against frequency is constant at any point along the curve. Also that the unity gain (0dB) frequency also determines the gain of the amplifier at any point along the curve. This constant is generally known as the Gain Bandwidth Product or GBP. Therefore:

GBP = Gain x Bandwidth = A x BW

For example, from the graph above the gain of the amplifier at 100kHz is given as 20dB or 10, then the gain bandwidth product is calculated as:

GBP = A x BW = 10 x 100,000Hz = 1,000,000.

Similarly, the operational amplifiers gain at 1kHz = 60dB or 1000, therefore the GBP is given as:

GBP = A x BW = 1,000 x 1,000Hz = 1,000,000. The same!.

The Voltage Gain (AV) of the operational amplifier can be found using the following formula:

and in Decibels or (dB) is given as:

An Operational Amplifiers Bandwidth

The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% or -3dB (where 0dB is the maximum) of its maximum output value as shown below.

Here we have used the 40dB line as an example. The -3dB or 70.7% of Vmax down point from the frequency response curve is given as 37dB. Taking a line across until it intersects with the main GBP curve gives us a frequency point just above the 10kHz line at about 12 to 15kHz. We can now calculate this more accurately as we already know the GBP of the amplifier, in this particular case 1MHz.

Operational Amplifier Example No1.

Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as:

37 = 20 log (A)   therefore, A = anti-log (37 ÷ 20) = 70.8

GBP ÷ A = Bandwidth,  therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz

Then the bandwidth of the amplifier at a gain of 40dB is given as 14kHz as previously predicted from the graph.

Operational Amplifier Example No2.

If the gain of the operational amplifier was reduced by half to say 20dB in the above frequency response curve, the -3dB point would now be at 17dB. This would then give the operational amplifier an overall gain of 7.08, therefore A = 7.08.

If we use the same formula as above, this new gain would give us a bandwidth of approximately 141.2kHz, ten times more than the frequency given at the 40dB point. It can therefore be seen that by reducing the overall “open loop gain” of an operational amplifier its bandwidth is increased and visa versa.

In other words, an operational amplifiers bandwidth is inversely proportional to its gain, ( A 1/∞ BW ). Also, this -3dB corner frequency point is generally known as the “half power point”, as the output power of the amplifier is at half its maximum value as shown:

Operational Amplifiers Summary

We know now that an Operational amplifiers is a very high gain DC differential amplifier that uses one or more external feedback networks to control its response and characteristics. We can connect external resistors or capacitors to the op-amp in a number of different ways to form basic “building Block” circuits such as, Inverting, Non-Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type amplifiers.

Op-amp Symbol

An “ideal” or perfect operational amplifier is a device with certain special characteristics such as infinite open-loop gain AO, infinite input resistance RIN, zero output resistance ROUT, infinite bandwidth 0 to ∞ and zero offset (the output is exactly zero when the input is zero).

There are a very large number of operational amplifier IC’s available to suit every possible application from standard bipolar, precision, high-speed, low-noise, high-voltage, etc, in either standard configuration or with internal Junction FET transistors.

Operational amplifiers are available in IC packages of either single, dual or quad op-amps within one single device. The most commonly available and used of all operational amplifiers in basic electronic kits and projects is the industry standard μA-741.

In the next tutorial about Operational Amplifiers, we will use negative feedback connected around the op-amp to produce a standard closed-loop amplifier circuit called an Inverting Amplifier circuit that produces an output signal which is 180o “out-of-phase” with the input.

Inverting Operational Amplifier

We saw in the last tutorial that the Open Loop Gain, ( Avo ) of an operational amplifier can be very high, as much as 1,000,000 (120dB) or more.

                                            

However, this very high gain is of no real use to us as it makes the amplifier both unstable and hard to control as the smallest of input signals, just a few micro-volts, (μV) would be enough to cause the output voltage to saturate and swing towards one or the other of the voltage supply rails losing complete control of the output.

As the open loop DC gain of an operational amplifier is extremely high we can therefore afford to lose some of this high gain by connecting a suitable resistor across the amplifier from the output terminal back to the inverting input terminal to both reduce and control the overall gain of the amplifier. This then produces and effect known commonly as Negative Feedback, and thus produces a very stable Operational Amplifier based system.

Negative Feedback is the process of “feeding back” a fraction of the output signal back to the input, but to make the feedback negative, we must feed it back to the negative or “inverting input” terminal of the op-amp using an external Feedback Resistor called Rƒ. This feedback connection between the output and the inverting input terminal forces the differential input voltage towards zero.

This effect produces a closed loop circuit to the amplifier resulting in the gain of the amplifier now being called its Closed-loop Gain. Then a closed-loop inverting amplifier uses negative feedback to accurately control the overall gain of the amplifier, but at a cost in the reduction of the amplifiers gain.

This negative feedback results in the inverting input terminal having a different signal on it than the actual input voltage as it will be the sum of the input voltage plus the negative feedback voltage giving it the label or term of a Summing Point. We must therefore separate the real input signal from the inverting input by using an Input Resistor, Rin.

As we are not using the positive non-inverting input this is connected to a common ground or zero voltage terminal as shown below, but the effect of this closed loop feedback circuit results in the voltage potential at the inverting input being equal to that at the non-inverting input producing a Virtual Earth summing point because it will be at the same potential as the grounded reference input. In other words, the op-amp becomes a “differential amplifier”.

Inverting Operational Amplifier Configuration

In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. When dealing with operational amplifiers there are two very important rules to remember about inverting amplifiers, these are: “No current flows into the input terminal” and that “V1 always equals V2”. However, in real world op-amp circuits both of these rules are slightly broken.

This is because the junction of the input and feedback signal ( X ) is at the same potential as the positive ( + ) input which is at zero volts or ground then, the junction is a “Virtual Earth”. Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.

We said above that there are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and these are.

• No Current Flows into the Input Terminals
• The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth)

Then by using these two rules we can derive the equation for calculating the closed-loop gain of an inverting amplifier, using first principles.

Current ( i ) flows through the resistor network as shown.

Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as.

and this can be transposed to give Vout as:

Linear Output

The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value.

The equation for the output voltage Vout also shows that the circuit is linear in nature for a fixed amplifier gain as Vout = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.

Another useful application of an inverting amplifier is that of a “transresistance amplifier” circuit. A Transresistance Amplifier also known as a “transimpedance amplifier”, is basically a current-to-voltage converter (Current “in” and Voltage “out”). They can be used in low-power applications to convert a very small current generated by a photo-diode or photo-detecting device etc, into a usable output voltage which is proportional to the input current as shown.

Transresistance Amplifier Circuit

The simple light-activated circuit above, converts a current generated by the photo-diode into a voltage. The feedback resistor Rƒ sets the operating voltage point at the inverting input and controls the amount of output. The output voltage is given as Vout = Is x Rƒ. Therefore, the output voltage is proportional to the amount of input current generated by the photo-diode.

Inverting Op-amp Example No1

Find the closed loop gain of the following inverting amplifier circuit.

Using the previously found formula for the gain of the circuit

we can now substitute the values of the resistors in the circuit as follows,

Rin = 10kΩ  and  Rƒ = 100kΩ.

and the gain of the circuit is calculated as: -Rƒ/Rin = 100k/10k = -10.

Therefore, the closed loop gain of the inverting amplifier circuit above is given -10 or 20dB (20log(10)).

Inverting Op-amp Example No2

The gain of the original circuit is to be increased to 40 (32dB), find the new values of the resistors required.

Assuming that the input resistor is to remain at the same value of 10KΩ, then by re-arranging the closed loop voltage gain formula we can find the new value required for the feedback resistor Rƒ.

   Gain = Rƒ/Rin

therefore,   Rƒ = Gain x Rin

  Rƒ = 40 x 10,000

  Rƒ = 400,000 or 400KΩ

The new values of resistors required for the circuit to have a gain of 40 would be:

 Rin = 10KΩ  and  Rƒ = 400KΩ.

The formula could also be rearranged to give a new value of Rin, keeping the same value of Rƒ.

One final point to note about the Inverting Amplifier configuration for an operational amplifier, if the two resistors are of equal value, Rin = Rƒ  then the gain of the amplifier will be -1 producing a complementary form of the input voltage at its output as Vout = -Vin. This type of inverting amplifier configuration is generally called a Unity Gain Inverter of simply an Inverting Buffer.

In the next tutorial about Operational Amplifiers, we will analyse the complement of the Inverting Amplifier operational amplifier circuit called the Non-inverting Amplifier that produces an output signal which is “in-phase” with the input.

Non-inverting Operational Amplifier

The second basic configuration of an operational amplifier circuit is that of a Non-inverting Operational Amplifier design.

                                                 

In this configuration, the input voltage signal, ( VIN ) is applied directly to the non-inverting ( + ) input terminal which means that the output gain of the amplifier becomes “Positive” in value in contrast to the “Inverting Amplifier” circuit we saw in the last tutorial whose output gain is negative in value. The result of this is that the output signal is “in-phase” with the input signal.

Feedback control of the non-inverting operational amplifier is achieved by applying a small part of the output voltage signal back to the inverting ( – ) input terminal via a Rƒ – R2 voltage divider network, again producing negative feedback. This closed-loop configuration produces a non-inverting amplifier circuit with very good stability, a very high input impedance, Rin approaching infinity, as no current flows into the positive input terminal, (ideal conditions) and a low output impedance, Rout as shown below.

Non-inverting Operational Amplifier Configuration

In the previous Inverting Amplifier tutorial, we said that for an ideal op-amp “No current flows into the input terminal” of the amplifier and that “V1 always equals V2”. This was because the junction of the input and feedback signal ( V1 ) are at the same potential.

In other words the junction is a “virtual earth” summing point. Because of this virtual earth node the resistors, Rƒ and R2 form a simple potential divider network across the non-inverting amplifier with the voltage gain of the circuit being determined by the ratios of R2 and Rƒ as shown below.

Equivalent Potential Divider Network

Then using the formula to calculate the output voltage of a potential divider network, we can calculate the closed-loop voltage gain ( A V ) of the Non-inverting Amplifier as follows:

Then the closed loop voltage gain of a Non-inverting Operational Amplifier will be given as:

We can see from the equation above, that the overall closed-loop gain of a non-inverting amplifier will always be greater but never less than one (unity), it is positive in nature and is determined by the ratio of the values of Rƒ and R2.

If the value of the feedback resistor Rƒ is zero, the gain of the amplifier will be exactly equal to one (unity). If resistor R2 is zero the gain will approach infinity, but in practice it will be limited to the operational amplifiers open-loop differential gain, ( Ao ).

We can easily convert an inverting operational amplifier configuration into a non-inverting amplifier configuration by simply changing the input connections as shown.

Voltage Follower (Unity Gain Buffer)

If we made the feedback resistor, Rƒ equal to zero, (Rƒ = 0), and resistor R2 equal to infinity, (R2 = ∞), then the circuit would have a fixed gain of “1” as all the output voltage would be present on the inverting input terminal (negative feedback). This would then produce a special type of the non-inverting amplifier circuit called a Voltage Followeror also called a “unity gain buffer”.

As the input signal is connected directly to the non-inverting input of the amplifier the output signal is not inverted resulting in the output voltage being equal to the input voltage, Vout = Vin. This then makes the voltage follower circuit ideal as a Unity Gain Buffer circuit because of its isolation properties.

The advantage of the unity gain voltage follower is that it can be used when impedance matching or circuit isolation is more important than amplification as it maintains the signal voltage. The input impedance of the voltage follower circuit is very high, typically above 1MΩ as it is equal to that of the operational amplifiers input resistance times its gain ( Rin x Ao ). Also its output impedance is very low since an ideal op-amp condition is assumed.

Non-inverting Voltage Follower

In this non-inverting circuit configuration, the input impedance Rin has increased to infinity and the feedback impedance Rƒ reduced to zero. The output is connected directly back to the negative inverting input so the feedback is 100% and Vin is exactly equal to Vout giving it a fixed gain of 1 or unity. As the input voltage Vin is applied to the non-inverting input the gain of the amplifier is given as:

Since no current flows into the non-inverting input terminal the input impedance is infinite (ideal op-amp) and also no current flows through the feedback loop so any value of resistance may be placed in the feedback loop without affecting the characteristics of the circuit as no voltage is dissipated across it, zero current flows, zero voltage drop, zero power loss.

As the input current is zero giving zero input power, the voltage follower can provide a large power gain. However in most real unity gain buffer circuits a low value (typically 1kΩ) resistor is required to reduce any offset input leakage currents, and also if the operational amplifier is of a current feedback type.

The voltage follower or unity gain buffer is a special and very useful type of Non-inverting amplifier circuit that is commonly used in electronics to isolated circuits from each other especially in High-order state variable or Sallen-Key type active filters to separate one filter stage from the other. Typical digital buffer IC’s available are the 74LS125 Quad 3-state buffer or the more common 74LS244 Octal buffer.

One final thought, the closed loop voltage gain of a voltage follower circuit is “1” or Unity. The open loop voltage gain of an operational amplifier with no feedback is Infinite. Then by carefully selecting the feedback components we can control the amount of gain produced by a non-inverting operational amplifier anywhere from one to infinity.

Thus far we have analysed an inverting and non-inverting amplifier circuit that has just one input signal, Vin. In the next tutorial about Operational Amplifiers, we will examine the effect of the output voltage, Vout by connecting more inputs to the amplifier. This then produces another common type of operational amplifier circuit called a Summing Amplifier which can be used to “add” together the voltages present on its inputs.

The Summing Amplifier

The Summing Amplifier is another type of operational amplifier circuit configuration that is used to combine the voltages present on two or more inputs into a single output voltage

                                  

We saw previously in the inverting operational amplifier that the inverting amplifier has a single input voltage, (Vin) applied to the inverting input terminal. If we add more input resistors to the input, each equal in value to the original input resistor, (Rin) we end up with another operational amplifier circuit called a Summing Amplifier, “summing inverter” or even a “voltage adder” circuit as shown below.

Summing Amplifier Circuit

In this simple summing amplifier circuit, the output voltage, ( Vout ) now becomes proportional to the sum of the input voltages, V1, V2, V3, etc. Then we can modify the original equation for the inverting amplifier to take account of these new inputs thus:

However, if all the input impedances, ( Rin ) are equal in value, we can simplify the above equation to give an output voltage of:

Summing Amplifier Equation

We now have an operational amplifier circuit that will amplify each individual input voltage and produce an output voltage signal that is proportional to the algebraic “SUM” of the three individual input voltages V1, V2 and V3. We can also add more inputs if required as each individual input “see’s” their respective resistance, Rin as the only input impedance.

This is because the input signals are effectively isolated from each other by the “virtual earth” node at the inverting input of the op-amp. A direct voltage addition can also be obtained when all the resistances are of equal value and Rƒ is equal to Rin.

Note that when the summing point is connected to the inverting input of the op-amp the circuit will produce the negative sum of any number of input voltages. Likewise, when the summing point is connected to the non-inverting input of the op-amp, it will produce the positive sum of the input voltages.

A Scaling Summing Amplifier can be made if the individual input resistors are “NOT” equal. Then the equation would have to be modified to:

To make the math’s a little easier, we can rearrange the above formula to make the feedback resistor RF the subject of the equation giving the output voltage as:

This allows the output voltage to be easily calculated if more input resistors are connected to the amplifiers inverting input terminal. The input impedance of each individual channel is the value of their respective input resistors, ie, R1, R2, R3 … etc.

Sometimes we need a summing circuit to just add together two or more voltage signals without any amplification. By putting all of the resistances of the circuit above to the same value R, the op-amp will have a voltage gain of unity and an output voltage equal to the direct sum of all the input voltages as shown:

The Summing Amplifier is a very flexible circuit indeed, enabling us to effectively “Add” or “Sum” (hence its name) together several individual input signals. If the inputs resistors, R1, R2, R3 etc, are all equal a “unity gain inverting adder” will be made. However, if the input resistors are of different values a “scaling summing amplifier” is produced which will output a weighted sum of the input signals.

Summing Amplifier Example No1

Find the output voltage of the following Summing Amplifier circuit.

Summing Amplifier

Using the previously found formula for the gain of the circuit

We can now substitute the values of the resistors in the circuit as follows,

We know that the output voltage is the sum of the two amplified input signals and is calculated as:

Then the output voltage of the Summing Amplifier circuit above is given as -45 mV and is negative as its an inverting amplifier.

Summing Amplifier Applications

So what can we use summing amplifiers for?. If the input resistances of a summing amplifier are connected to potentiometers the individual input signals can be mixed together by varying amounts.

For example, measuring temperature, you could add a negative offset voltage to make the output voltage or display read “0” at the freezing point or produce an audio mixer for adding or mixing together individual waveforms (sounds) from different source channels (vocals, instruments, etc) before sending them combined to an audio amplifier.

Summing Amplifier Audio Mixer

Another useful application of a Summing Amplifier is as a weighted sum digital-to-analogue converter. If the input resistors, Rin of the summing amplifier double in value for each input, for example, 1kΩ, 2kΩ, 4kΩ, 8kΩ, 16kΩ, etc, then a digital logical voltage, either a logic level “0” or a logic level “1” on these inputs will produce an output which is the weighted sum of the digital inputs. Consider the circuit below.

Digital to Analogue Converter

Of course this is a simple example. In this DAC summing amplifier circuit, the number of individual bits that make up the input data word, and in this example 4-bits, will ultimately determine the output step voltage as a percentage of the full-scale analogue output voltage.

Also, the accuracy of this full-scale analogue output depends on voltage levels of the input bits being consistently 0V for “0” and consistently 5V for “1” as well as the accuracy of the resistance values used for the input resistors, Rin.

Fortunately to overcome these errors, at least on our part, commercially available Digital-to Analogue and Analogue-to Digital devices are readily available with highly accurate resistor ladder networks already built-in.

In the next tutorial about operational amplifiers, we will examine the effect of the output voltage, Vout when a signal voltage is connected to the inverting input and the non-inverting input at the same time to produce another common type of operational amplifier circuit called a Differential Amplifier which can be used to “subtract” the voltages present on its inputs.

The Differential Amplifier

The differential amplifier amplifies the voltage difference present on its inverting and non-inverting inputs

                                                

Thus far we have used only one of the operational amplifiers inputs to connect to the amplifier, using either the “inverting” or the “non-inverting” input terminal to amplify a single input signal with the other input being connected to ground.

But as a standard operational amplifier has two inputs, inverting and no-inverting, we can also connect signals to both of these inputs at the same time producing another common type of operational amplifier circuit called a Differential Amplifier.

Basically, as we saw in the first tutorial about operational amplifiers, all op-amps are “Differential Amplifiers” due to their input configuration. But by connecting one voltage signal onto one input terminal and another voltage signal onto the other input terminal the resultant output voltage will be proportional to the “Difference” between the two input voltage signals of V1 and V2.

Then differential amplifiers amplify the difference between two voltages making this type of operational amplifier circuit a Subtractor unlike a summing amplifier which adds or sums together the input voltages. This type of operational amplifier circuit is commonly known as a Differential Amplifier configuration and is shown below:

Differential Amplifier

By connecting each input in turn to 0v ground we can use superposition to solve for the output voltage Vout. Then the transfer function for a Differential Amplifier circuit is given as:

When resistors, R1 = R2 and R3 = R4 the above transfer function for the differential amplifier can be simplified to the following expression:

Differential Amplifier Equation

If all the resistors are all of the same ohmic value, that is: R1 = R2 = R3 = R4 then the circuit will become a Unity Gain Differential Amplifier and the voltage gain of the amplifier will be exactly one or unity. Then the output expression would simply be Vout = V2 – V1.

Also note that if input V1 is higher than input V2 the output voltage sum will be negative, and if V2 is higher than V1, the output voltage sum will be positive.

The Differential Amplifier circuit is a very useful op-amp circuit and by adding more resistors in parallel with the input resistors R1 and R3, the resultant circuit can be made to either “Add” or “Subtract” the voltages applied to their respective inputs. One of the most common ways of doing this is to connect a “Resistive Bridge” commonly called a Wheatstone Bridge to the input of the amplifier as shown below.

Wheatstone Bridge Differential Amplifier

The standard Differential Amplifier circuit now becomes a differential voltage comparator by “Comparing” one input voltage to the other. For example, by connecting one input to a fixed voltage reference set up on one leg of the resistive bridge network and the other to either a “Thermistor” or a “Light Dependant Resistor” the amplifier circuit can be used to detect either low or high levels of temperature or light as the output voltage becomes a linear function of the changes in the active leg of the resistive bridge and this is demonstrated below.

Light Activated Differential Amplifier

Here the circuit above acts as a light-activated switch which turns the output relay either “ON” or “OFF” as the light level detected by the LDR resistor exceeds or falls below some pre-set value. A fixed voltage reference is applied to the non-inverting input terminal of the op-amp via the R1 – R2 voltage divider network.

The voltage value at V1 sets the op-amps trip point with a feed back potentiometer, VR2used to set the switching hysteresis. That is the difference between the light level for “ON” and the light level for “OFF”.

The second leg of the differential amplifier consists of a standard light dependant resistor, also known as a LDR, photoresistive sensor that changes its resistive value (hence its name) with the amount of light on its cell as their resistive value is a function of illumination.

The LDR can be any standard type of cadmium-sulphide (cdS) photoconductive cell such as the common NORP12 that has a resistive range of between about 500Ω in sunlight to about 20kΩ’s or more in the dark.

The NORP12 photoconductive cell has a spectral response similar to that of the human eye making it ideal for use in lighting control type applications. The photocell resistance is proportional to the light level and falls with increasing light intensity so therefore the voltage level at V2 will also change above or below the switching point which can be determined by the position of VR1.

Then by adjusting the light level trip or set position using potentiometer VR1 and the switching hysteresis using potentiometer, VR2 an precision light-sensitive switch can be made. Depending upon the application, the output from the op-amp can switch the load directly, or use a transistor switch to control a relay or the lamps themselves.

It is also possible to detect temperature using this type of simple circuit configuration by replacing the light dependant resistor with a thermistor. By interchanging the positions of VR1 and the LDR, the circuit can be used to detect either light or dark, or heat or cold using a thermistor.

One major limitation of this type of amplifier design is that its input impedances are lower compared to that of other operational amplifier configurations, for example, a non-inverting (single-ended input) amplifier.

Each input voltage source has to drive current through an input resistance, which has less overall impedance than that of the op-amps input alone. This may be good for a low impedance source such as the bridge circuit above, but not so good for a high impedance source.

One way to overcome this problem is to add a Unity Gain Buffer Amplifier such as the voltage follower seen in the previous tutorial to each input resistor. This then gives us a differential amplifier circuit with very high input impedance and low output impedance as it consists of two non-inverting buffers and one differential amplifier. This then forms the basis for most “Instrumentation Amplifiers”.

Instrumentation Amplifier

Instrumentation Amplifiers (in-amps) are very high gain differential amplifiers which have a high input impedance and a single ended output. Instrumentation amplifiers are mainly used to amplify very small differential signals from strain gauges, thermocouples or current sensing devices in motor control systems.

Unlike standard operational amplifiers in which their closed-loop gain is determined by an external resistive feedback connected between their output terminal and one input terminal, either positive or negative, “instrumentation amplifiers” have an internal feedback resistor that is effectively isolated from its input terminals as the input signal is applied across two differential inputs, V1 and V2.

The instrumentation amplifier also has a very good common mode rejection ratio, CMRR (zero output when V1 = V2) well in excess of 100dB at DC. A typical example of a three op-amp instrumentation amplifier with a high input impedance ( Zin ) is given below:

High Input Impedance Instrumentation Amplifier

The two non-inverting amplifiers form a differential input stage acting as buffer amplifiers with a gain of 1 + 2R2/R1 for differential input signals and unity gain for common mode input signals. Since amplifiers A1 and A2 are closed loop negative feedback amplifiers, we can expect the voltage at Va to be equal to the input voltage V1. Likewise, the voltage at Vb to be equal to the value at V2.

As the op-amps take no current at their input terminals (virtual earth), the same current must flow through the three resistor network of R2, R1 and R2 connected across the op-amp outputs. This means then that the voltage on the upper end of R1 will be equal to V1 and the voltage at the lower end of R1 to be equal to V2.

This produces a voltage drop across resistor R1 which is equal to the voltage difference between inputs V1 and V2, the differential input voltage, because the voltage at the summing junction of each amplifier, Va and Vb is equal to the voltage applied to its positive inputs.

However, if a common-mode voltage is applied to the amplifiers inputs, the voltages on each side of R1 will be equal, and no current will flow through this resistor. Since no current flows through R1 (nor, therefore, through both R2 resistors, amplifiers A1 and A2 will operate as unity-gain followers (buffers). Since the input voltage at the outputs of amplifiers A1 and A2 appears differentially across the three resistor network, the differential gain of the circuit can be varied by just changing the value of R1.

The voltage output from the differential op-amp A3 acting as a subtractor, is simply the difference between its two inputs ( V2 – V1 ) and which is amplified by the gain of A3which may be one, unity, (assuming that R3 = R4). Then we have a general expression for overall voltage gain of the instrumentation amplifier circuit as:

Instrumentation Amplifier Equation

In the next tutorial about Operational Amplifiers, we will examine the effect of the output voltage, Vout when the feedback resistor is replaced with a frequency dependant reactance in the form of a capacitance. The addition of this feedback capacitance produces a non-linear operational amplifier circuit called an Integrating Amplifier.

The Integrator Amplifier

Operational amplifiers can be used as part of a positive or negative feedback amplifier or as an adder or subtractor type circuit using just pure resistances in both the input and the feedback loop.

                                         

But what if we where to change the purely resistive ( Rƒ ) feedback element of an inverting amplifier to that of a frequency dependant impedance, ( Z ) type complex element, such as a Capacitor, C. What would be the effect on the op-amps output voltage over its frequency range.

By replacing this feedback resistance with a capacitor we now have an RC Networkconnected across the operational amplifiers feedback path producing another type of operational amplifier circuit commonly called an Op-amp Integrator circuit as shown below.

Op-amp Integrator Circuit

As its name implies, the Op-amp Integrator is an operational amplifier circuit that performs the mathematical operation of Integration, that is we can cause the output to respond to changes in the input voltage over time as the op-amp integrator produces an output voltage which is proportional to the integral of the input voltage.

In other words the magnitude of the output signal is determined by the length of time a voltage is present at its input as the current through the feedback loop charges or discharges the capacitor as the required negative feedback occurs through the capacitor.

When a step voltage, Vin is firstly applied to the input of an integrating amplifier, the uncharged capacitor C has very little resistance and acts a bit like a short circuit allowing maximum current to flow via the input resistor, Rin as potential difference exists between the two plates. No current flows into the amplifiers input and point X is a virtual earth resulting in zero output. As the impedance of the capacitor at this point is very low, the gain ratio of Xc/Rin is also very small giving an overall voltage gain of less than one, ( voltage follower circuit ).

As the feedback capacitor, C begins to charge up due to the influence of the input voltage, its impedance Xc slowly increase in proportion to its rate of charge. The capacitor charges up at a rate determined by the RC time constant, ( τ ) of the series RC network. Negative feedback forces the op-amp to produce an output voltage that maintains a virtual earth at the op-amp’s inverting input.

Since the capacitor is connected between the op-amp’s inverting input (which is at earth potential) and the op-amp’s output (which is negative), the potential voltage, Vcdeveloped across the capacitor slowly increases causing the charging current to decrease as the impedance of the capacitor increases. This results in the ratio of Xc/Rinincreasing producing a linearly increasing ramp output voltage that continues to increase until the capacitor is fully charged.

At this point the capacitor acts as an open circuit, blocking any more flow of DC current. The ratio of feedback capacitor to input resistor ( Xc/Rin ) is now infinite resulting in infinite gain. The result of this high gain (similar to the op-amps open-loop gain), is that the output of the amplifier goes into saturation as shown below. (Saturation occurs when the output voltage of the amplifier swings heavily to one voltage supply rail or the other with little or no control in between).

The rate at which the output voltage increases (the rate of change) is determined by the value of the resistor and the capacitor, “RC time constant“. By changing this RC time constant value, either by changing the value of the Capacitor, C or the Resistor, R, the time in which it takes the output voltage to reach saturation can also be changed for example.

If we apply a constantly changing input signal such as a square wave to the input of an Integrator Amplifier then the capacitor will charge and discharge in response to changes in the input signal. This results in the output signal being that of a sawtooth waveform whose output is affected by the RC time constant of the resistor/capacitor combination because at higher frequencies, the capacitor has less time to fully charge. This type of circuit is also known as a Ramp Generator and the transfer function is given below.

Op-amp Integrator Ramp Generator

We know from first principals that the voltage on the plates of a capacitor is equal to the charge on the capacitor divided by its capacitance giving Q/C. Then the voltage across the capacitor is output Vout therefore: -Vout = Q/C. If the capacitor is charging and discharging, the rate of charge of voltage across the capacitor is given as:

But dQ/dt is electric current and since the node voltage of the integrating op-amp at its inverting input terminal is zero, X = 0, the input current I(in) flowing through the input resistor, Rin is given as:

The current flowing through the feedback capacitor C is given as:

Assuming that the input impedance of the op-amp is infinite (ideal op-amp), no current flows into the op-amp terminal. Therefore, the nodal equation at the inverting input terminal is given as:

From which we derive an ideal voltage output for the Op-amp Integrator as:

To simplify the math’s a little, this can also be re-written as:

Where: ω = 2πƒ and the output voltage Vout is a constant 1/RC times the integral of the input voltage Vin with respect to time. The minus sign ( – ) indicates a 180o phase shift because the input signal is connected directly to the inverting input terminal of the op-amp.

The AC or Continuous Op-amp Integrator

If we changed the above square wave input signal to that of a sine wave of varying frequency the Op-amp Integrator performs less like an integrator and begins to behave more like an active “Low Pass Filter”, passing low frequency signals while attenuating the high frequencies.

At 0Hz or DC, the capacitor acts like an open circuit blocking any feedback voltage resulting in very little negative feedback from the output back to the input of the amplifier. Then with just the feedback capacitor, C, the amplifier effectively is connected as a normal open-loop amplifier which has very high open-loop gain resulting in the output voltage saturating.

This circuit connects a high value resistance in parallel with a continuously charging and discharging capacitor. The addition of this feedback resistor, R2 across the capacitor, C gives the circuit the characteristics of an inverting amplifier with finite closed-loop gain of R2/R1. The result is at very low frequencies the circuit acts as an standard integrator, while at higher frequencies the capacitor shorts out the feedback resistor, R2 due to the effects of capacitive reactance reducing the amplifiers gain.

The AC Op-amp Integrator with DC Gain Control

Unlike the DC integrator amplifier above whose output voltage at any instant will be the integral of a waveform so that when the input is a square wave, the output waveform will be triangular. For an AC integrator, a sinusoidal input waveform will produce another sine wave as its output which will be 90o out-of-phase with the input producing a cosine wave.

Further more, when the input is triangular, the output waveform is also sinusoidal. This then forms the basis of a Active Low Pass Filter as seen before in the filters section tutorials with a corner frequency given as.

In the next tutorial about Operational Amplifiers, we will look at another type of operational amplifier circuit which is the opposite or complement of the Op-amp Integrator circuit above called the Differentiator Amplifier.

As its name implies, the differentiator amplifier produces an output signal which is the mathematical operation of differentiation, that is it produces a voltage output which is proportional to the input voltage’s rate-of-change and the current flowing through the input capacitor.

The Differentiator Amplifier

The basic operational amplifier differentiator circuit is the exact opposite to that of the op-amp integrator circuit that we looked at in the previous tutorial

                                       

Here, the position of the capacitor and resistor have been reversed and now the reactance, Xc is connected to the input terminal of the inverting amplifier while the resistor, Rƒ forms the negative feedback element across the operational amplifier as normal.

This operational amplifier circuit performs the mathematical operation of Differentiation, that is it “produces a voltage output which is directly proportional to the input voltage’s rate-of-change with respect to time“. In other words the faster or larger the change to the input voltage signal, the greater the input current, the greater will be the output voltage change in response, becoming more of a “spike” in shape.

As with the integrator circuit, we have a resistor and capacitor forming an RC Networkacross the operational amplifier and the reactance ( Xc ) of the capacitor plays a major role in the performance of a Op-amp Differentiator.

Op-amp Differentiator Circuit

The input signal to the differentiator is applied to the capacitor. The capacitor blocks any DC content so there is no current flow to the amplifier summing point, X resulting in zero output voltage. The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependant on the rate of change of the input signal.

At low frequencies the reactance of the capacitor is “High” resulting in a low gain ( Rƒ/Xc ) and low output voltage from the op-amp. At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier.

However, at high frequencies an op-amp differentiator circuit becomes unstable and will start to oscillate. This is due mainly to the first-order effect, which determines the frequency response of the op-amp circuit causing a second-order response which, at high frequencies gives an output voltage far higher than what would be expected. To avoid this the high frequency gain of the circuit needs to be reduced by adding an additional small value capacitor across the feedback resistor Rƒ.

Ok, some math’s to explain what’s going on!. Since the node voltage of the operational amplifier at its inverting input terminal is zero, the current, i flowing through the capacitor will be given as:

The charge on the capacitor equals Capacitance x Voltage across the capacitor

The rate of change of this charge is:

but dQ/dt is the capacitor current, i

from which we have an ideal voltage output for the op-amp differentiator is given as:

Therefore, the output voltage Vout is a constant –Rƒ*C times the derivative of the input voltage Vin with respect to time. The minus sign (–) indicates a 180o phase shift because the input signal is connected to the inverting input terminal of the operational amplifier.

One final point to mention, the Op-amp Differentiator circuit in its basic form has two main disadvantages compared to the previous operational amplifier integrator circuit. One is that it suffers from instability at high frequencies as mentioned above, and the other is that the capacitive input makes it very susceptible to random noise signals and any noise or harmonics present in the source circuit will be amplified more than the input signal itself. This is because the output is proportional to the slope of the input voltage so some means of limiting the bandwidth in order to achieve closed-loop stability is required.

Op-amp Differentiator Waveforms

If we apply a constantly changing signal such as a Square-wave, Triangular or Sine-wave type signal to the input of a differentiator amplifier circuit the resultant output signal will be changed and whose final shape is dependant upon the RC time constant of the Resistor/Capacitor combination.

Improved Op-amp Differentiator Amplifier

The basic single resistor and single capacitor op-amp differentiator circuit is not widely used to reform the mathematical function of Differentiation because of the two inherent faults mentioned above, “Instability” and “Noise”. So in order to reduce the overall closed-loop gain of the circuit at high frequencies, an extra resistor, Rin is added to the input as shown below.

Improved Op-amp Differentiator Amplifier

Adding the input resistor Rin limits the differentiators increase in gain at a ratio of Rƒ/Rin. The circuit now acts like a differentiator amplifier at low frequencies and an amplifier with resistive feedback at high frequencies giving much better noise rejection.

Additional attenuation of higher frequencies is accomplished by connecting a capacitor Cƒ in parallel with the differentiator feedback resistor, Rƒ. This then forms the basis of a Active High Pass Filter as we have seen before in the filters section.

Operational Amplifier Building Blocks

We have seen that we can connect resistors to a basic operational amplifier to produce various inverting and non-inverting outputs and configurations along with their respective gains.

                                   

So to make things a little bit easier for all, here is a list of some of the “Basic Operational Amplifier Building Blocks” we can use to create different electronic circuits and filters.

The Voltage Follower

The Voltage Follower, also called a buffer dose not amplify or invert the input signal but instead provides isolation between two circuits. The input impedance is very high while the output impedance is low avoiding any loading effects within the circuit. As the output is connected back directly to one of the inputs, the overall gain of the buffer is +1and Vout = Vin.

The Voltage Follower Op-amp Circuit

 

The Op-amp Inverter

The Inverter, also called an inverting buffer is the opposite to that of the previous voltage follower. The inverter does not amplify if both resistances are equal but does invert the input signal. The input impedance is equal to R and the gain is -1 giving Vout = -Vin.

The Op-amp Inverter Circuit

 

The Non-inverting Amplifier

The Non-inverting Amplifier does not invert the input signal or produce an inverting signal but instead amplifies it by the ratio of: (RA + RB)/RB or commonly 1+(RA/RB). The input signal is connected to the non-inverting (+) input.

The Non-inverting Op-amp Circuit

 

The Inverting Amplifier

The Inverting Amplifier both inverts and amplifies the input signal by the ratio of -RA/RB. The gain of the amplifier is controlled by negative feedback using the feedback resistor RA and the input signal is fed to the inverting (–) input.

The Inverting Op-amp Circuit

 

The Bridge Amplifier

The inverting and non-inverting amplifier circuits from above can be connected together to form a bridge amplifier configuration. The input signal is common to both op-amps with the output voltage signal taken across the load resistor, RL which floats between the two outputs.

If the magnitudes of the two op-amp gains, A1 and A2 are equal to each other, then the output signal will be doubled as it is effectively the combination of the two individual amplifier gains.

The Bridge Op-amp Circuit

 

The Voltage Adder

The Adder, also called a summing amplifier, produces an inverted output voltage which is proportional to the sum of the input voltages V1 and V2. More inputs can be summed. If the input resistors are equal in value (R1 = R2 = R) then the summed output voltage is as given and the gain is +1. If the input resistors are unequal then the output voltage is a weighted sum and becomes:

Vout = -(V1(RA/R1) + V2(RA/R2) + etc.)

The Voltage Adder Op-amp Circuit

 

The Voltage Subtractor

The Subtractor also called a differential amplifier, uses both the inverting and non-inverting inputs to produce an output signal which is the difference between the two input voltages V1 and V2 allowing one signal to be subtracted from another. More inputs can be added to be subtracted if required.

If resistances are equal (R = R3 and RA = R4) then the output voltage is as given and the voltage gain is +1. If the input resistance are unequal the circuit becomes a differential amplifier producing a negative output when V1 is higher than V2 and a positive output when V1 is lower than V2.

The Voltage Subtractor Op-amp Circuit

 

The Op-amp Comparator

The Comparator has many uses but the most common is to compare the input voltage to a reference voltage and switch the output if the input voltage is above the reference voltage. If the input goes more positive than the reference voltage set by the voltage divider, Vin > Vref, the output changes state.

When the input voltage drops below the preset reference voltage and Vin < Vref, the output switches back. By using positive feedback the basic comparator circuit can easily be converted into a Schmitt Trigger to reduce oscillations around the switching point.

The Comparator Op-amp Circuit

 

Here are just some of the more common and basic operational amplifier building block configurations discussed in this section that we can use in electronic circuits. All the above circuits can be constructed using a variety of different op-amps including the famous 741 op-amp. I hope that this short tutorial about basic op-amp building blocks will help you to understand the different basic op-amp circuit configurations.

Op-amp Multivibrator

The Operational Amplifier or Op-amp for short, is a very versatile device that can be used in a variety of different electronic circuits and applications, from voltage amplifiers, to filters, to signal conditioners.

                                                    

But one very simple and extremely useful op-amp circuit based around any general purpose operational amplifier is the Astable Op-amp Multivibrator.

We saw in our tutorials about Sequential Logic that multivibrator circuits can be constructed using transistors, logic gates or from dedicated chips such as the NE555 timer. We also saw that the astable multivibrator switches continuously between its two unstable states without the need for any external triggering.

But the problem with using these components to produce an astable multivibrator circuit is that for transistor based astables, many additional components are required, digital astables can generally only be used in digital circuits, and the use of a 555 timer may not always give us a symmetrical output without additional biasing components. The Op-amp Multivibrator circuit however, can provide us with a good rectangular wave signal with the use of just four components, three resistors and a timing capacitor.

The Op-amp Multivibrator is an astable oscillator circuit that generates a rectangular output waveform using an RC timing network connected to the inverting input of the operational amplifier and a voltage divider network connected to the other non-inverting input.

Unlike the monostable or bistable, the astable multivibrator has two states, neither of which are stable as it is constantly switching between these two states with the time spent in each state controlled by the charging or discharging of the capacitor through a resistor.

In the op-amp multivibrator circuit the op-amp works as an analogue comparator. An op-amp comparator compares the voltages on its two inputs and gives a positive or negative output depending on whether the input is greater or less than some reference value, Vref.

However, because the open-loop op-amp comparator is very sensitive to the voltage changes on its inputs, the output can switch uncontrollably between its positive, +V(sat) and negative, -V(sat) supply rails whenever the input voltage being measured is near to the reference voltage, Vref.

To eliminate any erratic or uncontrolled switching operations, the op-amp used in the multivibrator circuit is configured as a closed-loop Schmitt Trigger circuit. Consider the circuit below.

Op-amp Schmitt Comparator

 

The op-amp comparator circuit above is configured as a Schmitt trigger that uses positive feedback provided by resistors R1 and R2 to generate hysteresis. As this resistive network is connected between the amplifiers output and non-inverting (+) input, when Vout is saturated at the positive supply rail, a positive voltage is applied to the op-amps non-inverting input. Likewise, when Vout is saturated to the negative supply rail, a negative voltage is applied to the op-amps non-inverting input.

As the two resistors are configured across the op-amps output as a voltage divider network, the reference voltage, Vref will therefore be dependant upon the fraction of output voltage fed back to the non-inverting input. This feedback fraction, β is given as:

 

Where +V(sat) is the positive op-amp DC saturation voltage and -V(sat) is the negative op-amp DC saturation voltage.

Then we can see that the positive or upper reference voltage, +Vref (i.e. the maximum positive value for the voltage at the inverting input) is given as: +Vref = +V(sat)β while the negative or lower reference voltage (i.e. the maximum negative value for the voltage at the inverting input) is given as: -Vref = -V(sat)β.

So if Vin exceeds +Vref, the op-amp switches state and the output voltage drops to its negative DC saturation voltage. Likewise when the input voltage falls below -Vref, the op-amp switches state once again and the output voltage will switch from the negative saturation voltage back to the positive DC saturation voltage. The amount of built-in hysteresis given by the Schmitt comparator as it switches between the two saturation voltages is defined by the difference between the two trigger reference voltages as: VHYSTERESIS = +Vref - (-Vref).

Sinusoidal to Rectangular Conversion

One of the many uses of a Schmitt trigger comparator, other than as an op-amp multivibrator, is that we can use it to convert any periodic sinusoidal waveform into a rectangular waveform providing the value of the sinusoid is greater than the voltage reference point.

In fact the Schmitt comparator will always produce a rectangular output waveform independent of the input signal waveform. In other words, the voltage input does not have to be a sinusoid, it could be any wave shape or complex waveform. Consider the circuit below.

Sinusoidal to Rectangular Converter

 

As the input waveform will be periodical and have an amplitude sufficiently greater than its reference voltage, Vref, the output rectangular waveform will always have the same period, T and therefore frequency, ƒ as the input waveform.

By replacing either resistor R1 or R2 with a potentiometer we could adjust the feedback fraction, β and therefore the reference voltage value at the non-inverting input to cause the op-amp to change state anywhere from zero to 90o of each half cycle so long as the reference voltage, Vref remained below the maximum amplitude of the input signal.

Op-amp Multivibrator

We can take this idea of converting a periodic waveform into a rectangular output one step further by replacing the sinusoidal input with an RC timing circuit connected across the op-amps output. This time, instead of a sinusoidal waveform being used to trigger the op-amp, we can use the capacitors charging voltage, Vc to change the output state of the op-amp as shown.

Op-amp Multivibrator Circuit

 

So how does it work. Firstly lets assume that the capacitor is fully discharged and the output of the op-amp is saturated at the positive supply rail. The capacitor, C starts to charge up from the output voltage, Vout through resistor, R at a rate determined by their RC time constant.

We know from our tutorials about RC circuits that the capacitor wants to charge up fully to the value of Vout (which is +V(sat)) within five time constants. However, as soon as the capacitors charging voltage at the op-amps inverting (-) terminal is equal to or greater than the voltage at the non-inverting terminal (the op-amps output voltage fraction divided between resistors R1 and R2), the output will change state and be driven to the opposing negative supply rail.

But the capacitor, which has been happily charging towards the positive supply rail (+V(sat)), now sees a negative voltage, -V(sat) across its plates. This sudden reversal of the output voltage causes the capacitor to discharge toward the new value of Vout at a rate dictated again by their RC time constant.

Op-amp Multivibrator Voltages

 

Once the op-amps inverting terminal reaches the new negative reference voltage, -Vrefat the non-inverting terminal, the op-amp once again changes state and the output is driven to the opposing supply rail voltage, +V(sat). The capacitor now see’s a positive voltage across its plates and the charging cycle begins again. Thus, the capacitor is constantly charging and discharging creating an astable op-amp multivibrator output.

The period of the output waveform is determined by the RC time constant of the two timing components and the feedback ratio established by the R1, R2 voltage divider network which sets the reference voltage level. If the positive and negative values of the amplifiers saturation voltage have the same magnitude, then t1 = t2 and the expression to give the period of oscillation becomes:

 

Then we can see from the above equation that the frequency of oscillation for an Op-amp Multivibrator circuit not only depends upon the RC time constant but also upon the feedback fraction. However, if we used resistor values that gave a feedback fraction of 0.462, (β = 0.462), then the frequency of oscillation of the circuit would be equal to just 1/2RC as shown because the linear log term becomes equal to one.

Example No1

An op-amp multivibrator circuit is constructed using the following components. R1 = 35kΩ, R2 = 30kΩ, R = 50kΩ and C = 0.01uF. Calculate the circuits frequency of oscillation.

 

 

Then the frequency of oscillation is calculated as 1kHz. When β = 0.462, this frequency can be calculated directly as: ƒ = 1/2RC. Also when the two feedback resistors are the same, that is R1 = R2, the feedback fraction is equal to 3 and the frequency of oscillation becomes: ƒ = 1/2.2RC.

We can take this op-amp multivibrator circuit one step further by replacing one of the feedback resistors with a potentiometer to produce a variable frequency op-amp multivibrator as shown.

Variable Op-amp Multivibrator

 

By adjusting the central potentiometer between β1 and β2 the output frequency will change by the following amounts.

Potentiometer wiper at β1

Potentiometer wiper at β2

 

Then in this simple example we can produce an operational amplifier multivibrator circuit that can produce a variable output rectangular waveform from 100Hz to 1.2kHz, or any frequency range we require just by changing the RC component values.

We have seen above that an Op-amp Multivibrator circuit can be constructed using a standard operational amplifier, such as the 741, and a few additional components. These voltage controlled non-sinusoidal relaxation oscillators are generally limited to a few hundred kilo-hertz (kHz) because the op-amp does not have the required bandwidth, but nevertheless they still make excellent oscillators.

Operational Amplifiers Summary

We can conclude our section and look at Operational Amplifiers with the following summary of the different types of Op-amp circuits and their different configurations discussed throughout this op-amp tutorial section.

                                     

                                                      

Operational Amplifier General Conditions

• • The Operational Amplifier, or Op-amp as it is most commonly called, can be an ideal amplifier with infinite Gain and Bandwidth when used in the Open-loop mode with typical DC gains of well over 100,000 or 100dB.
• • The basic Op-amp construction is of a 3-terminal device, 2-inputs and 1-output, (excluding power connections).
• • An Operational Amplifier operates from either a dual positive ( +V ) and an corresponding negative ( -V ) supply, or they can operate from a single DC supply voltage.
• • The two main laws associated with the operational amplifier are that it has an infinite input impedance, ( Z = ∞ ) resulting in “No current flowing into either of its two inputs” and zero input offset voltage V1 = V2.
• • An operational amplifier also has zero output impedance, ( Z = 0 ).
• • Op-amps sense the difference between the voltage signals applied to their two input terminals and then multiply it by some pre-determined Gain, ( A ).
• • This Gain, ( A ) is often referred to as the amplifiers “Open-loop Gain”.
• • Closing the open loop by connecting a resistive or reactive component between the output and one input terminal of the op-amp greatly reduces and controls this open-loop gain.
• • Op-amps can be connected into two basic configurations, Inverting and Non-inverting.

The Two Basic Operational Amplifier Circuits

• For negative feedback, were the fed-back voltage is in “anti-phase” to the input the overall gain of the amplifier is reduced.
• For positive feedback, were the fed-back voltage is in “Phase” with the input the overall gain of the amplifier is increased.
• By connecting the output directly back to the negative input terminal, 100% feedback is achieved resulting in a Voltage Follower (buffer) circuit with a constant gain of 1 (Unity).
• Changing the fixed feedback resistor ( Rƒ ) for a Potentiometer, the circuit will have Adjustable Gain.

Operational Amplifier Gain

• The Open-loop gain called the Gain Bandwidth Product, or (GBP) can be very high and is a measure of how good an amplifier is.
• Very high GBP makes an operational amplifier circuit unstable as a micro volt input signal causes the output voltage to swing into saturation.
• By the use of a suitable feedback resistor, ( Rƒ ) the overall gain of the amplifier can be accurately controlled.

Differential and Summing Amplifiers

 

• By adding more input resistors to either the inverting or non-inverting inputs Voltage Adders or Summers can be made.
• Voltage follower op-amps can be added to the inputs of Differential amplifiers to produce high impedance Instrumentation amplifiers.
• The Differential Amplifier produces an output that is proportional to the difference between the two input voltages.

Differentiator and Integrator Operational Amplifier Circuits

 

• The Integrator Amplifier produces an output that is the mathematical operation of integration.
• The Differentiator Amplifier produces an output that is the mathematical operation of differentiation.
• Both the Integrator and Differentiator Amplifiers have a resistor and capacitor connected across the op-amp and are affected by its RC time constant.
• In their basic form, Differentiator Amplifiers suffer from instability and noise but additional components can be added to reduce the overall closed-loop gain.