Power Supply rejection Ratio (PSRR) specifies that if there is any change in the supply voltage, then how it will affect the output of the op-amp. For op-amp, if there is any change in the supply voltage, then it should not affect the output of the op-amp. With the change in the supply voltage, the output voltage of the op-amp will also change by a small margin. And this is specifically important when the input signal level is very small. This PSRR is specified in terms of the input offset voltage. That means with the change in the supply voltage, how the input offset voltage of the op-amp will change. And typically, the unit of this PSRR is μV / V.

Where,

ΔVio= change in the input offset voltage

ΔVs= change in the supply voltage

For example, for some op-amp if the PSRR is equal to 10 μV / V, it means that when the supply voltage will change by 1 volt, then the input offset voltage of that op-amp will change by a 10 μV. The change in the input offset voltage will lead to the change in the output of the op-amp.

For dual supply op-amps typically it is assumed that the change in the supply voltage is symmetrical. But if the change in the supply voltage is not symmetrical, then it will lead to the common mode error.

In the decibel this PSRR is defined as

Effect of Supply Voltage on input offset voltage of the op-amp

Internally, the first stage of the op-amp consist of differential amplifier. For the differential amplifier, if both the transistors are identical then if we apply the same input at both terminals, then output of the op-amp should be zero. But because of some mismatch between the two transistors, there will be some finite differential output. And that differential output will get amplified by the gain of the op-amp. Hence there will be some finite output voltage even if both input terminals are connected to the same input terminal. The input offset voltage is the additional input voltage that we need to apply between the two input terminals, to make the output of the op-amp zero.

With the variation in the supply voltage, the biasing of the differential amplifier will change and hence, the input offset voltage of the op-amp will also change.

The change in the input offset voltage will lead to the change in the output of the op-amp. If the op-amp is configured in the closed loop configuration (inverting or non-inverting), then the input offset voltage will get multiplied by the noise gain of the op-amp.

The Power Supply Rejection Ratio (PSRR) is the ability of the op-amp to withstand the change in the supply voltage. The smaller value of PSRR (μV/ V) is preferable. If PSRR is specified in dB, then larger value of PSRR is preferable.

PSRR with Frequency

PSRR value will also reduce with the frequency. That means if we have a ripple let’s say of 100 Hertz on top of the supply voltage, then that ripple will not be rejected by the op-amp as effectively as the DC voltage. And because of that, some fraction of that ripple will also appear at the output of the op-amp.

The below figure shows the typical PSRR curve with frequency. As the frequency increases, the PSRR (in dB) reduces.

Therefore, to reduce the effect of high frequency ripple on the output of the op-amp, it is advisable to use a well regulated supply voltage with the op-amp. And to avoid any high frequency noise in the output, the proper value of the decoupling capacitor should always be used with the op-amp. The decoupling capacitors provides the low impedance part to the high frequency noise. And in a way it reduces the effect of the high frequency noise at the output of the op-amp.

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Frequency Response of the Op-Amp

For the ideal op-amp, the gain is infinite and it has infinite bandwidth. But the actual op-amp has finite bandwidth and finite gain. And the gain versus frequency curve is shown in figure 1. The Y-axis on the curve is the voltage gain of the op-amp in dB, while the X-axis is the frequency in the logarithmic scale.

Fig. 1 Frequency Response of the operational amplifier

As shown in Fig.1, The gain of the op-amp is constant up to a certain frequency and beyond that frequency, the gain of the op-amp reduces at a constant rate of -20 dB/dec.

Cut-off Frequency of the op-amp: The frequency at which the gain of the op-amp reduces by 3dB from the maximum value is known as the cut-off frequency of the op-amp. As seen from the above frequency response curve of the op-amp, the cut-off frequency is very low. Typically for the op-amp, it used to be in the range of 10 to 100 Hz. And up to cut-off frequency, the op-amp provides very high gain.

Although we typically say that, the gain of the op-amp is very high. But actually, the op-amp provides a very high gain up to cut-off frequency. The reason is, all the op-amps are internally compensated. That means all the op-amps have an internal compensation capacitor. And this internal compensation capacitor ensures that the op-amp has a stable response at the high frequencies.

Because of this internal compensation capacitor, the op-amp has a single break frequency up to the gain of the op-amp reaches to unity. Without the internal compensation capacitor, the op-amp can have a multiple break frequency till the gain of the op-amp becomes unity. (As shown in Fig.2)

Fig.2 Multiple break-frequencies in the op-amp frequency response without internal compensation capacitor

The multiple break frequencies can occur because of the stray capacitances and load capacitance. And because of the multiple break frequencies, the op-amp becomes unstable at high frequency. And that’s why all op-amps are internally compensated. And because of this internal compensation, in the open-loop condition, the cut-off frequency of the op-amp is very low.

Unity Gain Frequency : The frequency where the gain of the op-amp is unity is called unity gain frequency.

As, shown in Fig.3, because of the internal compensation, it is easy to understand the behavior of the op-amp with frequency (particularly in the closed-loop configuration). And the product of gain and frequency remains constant till the unity gain frequency for the op-amp, which is known as the gain-bandwidth product of the op-amp.

Fig. 3 Gain-Bandwidth Product of Op-Amp

For example, as shown in Fig.3, at 1 kHz frequency, the gain of the op-amp is 60 dB = 10³. Therefore, the gain-bandwidth product (GBP) is 1000Hz x 10³ = 10⁶

On the other end, at 1MHz, the gain of the op-amp is 1. Therefore, the GBP is 10⁶.

The Gain Bandwidth Product

Using the gain-bandwidth product, it is easy to identify the cut-off frequency of the op-amp, in the closed-loop configuration. Let’s say in the closed-loop configuration, the gain of the op-amp is 40 dB (100). In that case, the frequency response of the op-amp is shown in Fig.4.

Fig.4 The Frequency Response of the op-amp in the closed loop configuration

As shown in Fig.4, the gain of the op-amp is flat up to a certain frequency. And then it starts reducing at 20 dB/dec. The frequency from where the gain starts reducing is known as the cut-off frequency in the closed-loop configuration. And it can be found using the Gain Bandwidth Product.

For example, the gain of the op-amp is 100. (40 dB) and the gain-bandwidth product is 10⁶. Therefore, the cut-off frequency in the closed-loop configuration is 10⁶ / 100 = 10 kHz. As, seen from the above calculation, when the op-amp is used in the closed-loop configuration, then the cut-off frequency of the op-amp increases. Or in other words, using the op-amp in the closed-loop configuration, the gain up to which we get a constant gain (Flat gain response) can be increased. Also, here the product of closed-loop gain, and the cut-off frequency is equal to Gain Bandwidth Product (GBP).

GBP = A_CL x f_CL

Using this gain-bandwidth product, at a particular closed-loop gain, we can find the frequency up to which the gain of the op-amp will remain constant. For example, in the above case, when the Gain Bandwidth Product of the op-amp is 10⁶ and closed-loop gain 100, then up to 10 kHz, the gain of the op-amp will remain constant. Beyond that, it will start reducing.

That means to use the op-amp at high frequency with high gain, the gain bandwidth product of the op-amp should be sufficient to provide the constant gain at the operating frequency.

For example, with a required gain of 40dB (100), if the op-amp needs to be operated at 100 kHz, then the Gain Bandwidth Product of the op-amp should be at least 100 x 10⁵ = 10⁷ = 10 MHz. And sometimes, it becomes a very costly solution to use the op-amp of a very high gain-bandwidth product.

Instead, by cascading multiple stages, the bandwidth (the usable frequency up to which the gain of the op-amp is almost constant) of the overall cascaded system can be increased.

Cascading of op-amps to increase the overall bandwidth

As shown in Fig.5, let’s say for one op-amp, the Gain Bandwidth Product is 10⁶. And the gain of the op-amp in the closed-loop configuration is set to 100. In that case, the cut-off frequency of the op-amp is 10⁶ / 100 = 10⁴ = 10 kHz.

Fig. 5 Closed loop cut-off frequency of the Non-inverting op-amp

That means, in this configuration, the op-amp can provide a fixed gain only upto 10 kHz frequency. If we want to use the op-amp at a higher frequency with the same gain, then we need to choose an op-amp of high gain-bandwidth product. But the same can be achieved using the cascade connection of two op-amps. As shown in Fig.6, the two op-amps are cascaded.

Fig. 6 Cascade connection of the two op-amps to increase the overall bandwidth

As shown in figure.6, the gain-bandwidth product of each op-amp is 10⁶. And the gain of each op-amp is set to 10. That means the combined gain of the two op-amps is approximately equal to 100.

But now the cut-off frequency of the overall cascaded system is approximately equal to 64 kHz. If we have used a single op-amp with gain of 100. Then the cut-off frequency of that op-amp would have been 10 kHz. But with the cascaded connection, now the usable frequency range has been increased.

If fc is the cut-off frequency of the single stage, then for n- cascaded stages, the cut-off frequency is

where, n- number of stages and fc is the cut-off frequency of the single stage

In the above expression, when we put fc = 100 kHz and n = 2, we get f’_cl = 64 kHz

That means instead of using a single stage op-amp, by using a multiple stages, the overall bandwidth of the op-amp can be increased for the same gain.

For more information about Gain Bandwidth Product, check this video tutorial.

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2. Inverting op-amp and the concept of Virtual Ground

3. Non-Inverting op-amp and the op-amp as buffer

4. Op-amp as summing amplifier

5. Op-Amp Gain Bandwidth Product

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Inverting Summing Amplifier

Fig.1 Inverting Summing Amplifier

As shown in Fig.1, the op-amp is used as a summing amplifier in the inverting configuration. The inputs to the op-amp (V1, V2, and V3) are applied using the resistors R1, R2, and R3 respectively. The output of the op-amp can be given as

Proof:

Here, assume the op-amp is an ideal op-amp. As shown in Fig.2, let’s say, the current flowing through resistor R1, R2 and R3 are I1, I2, and I3. And current flowing through resistor R_f is I_F.

Fig.2 Currents in the Inverting Summing Amplifier

For an ideal op-amp, no current is flowing into the op-amp terminal. So, applying KCL at node A, it can be written as

If R1 = R2 = R3 = R then

When R_f = R, then Vout = – (V₁ + V₂ + V₃)

And when R1 = R2 = R3 = R and the ratio of Rf and R is selected such that,

where n=number of inputs being applied to the inverting terminal.

Then it can be used as a averaging circuit. For example, in the above circuit when R₁= R₂ = R₃ = R and R = 3 R_f then Vo = – (V₁ + V₂ + V₃)/3

That means output is the average of the three input signals.

Applications of Summing Amplifier

• Summing, Averaging, and Scaling
• For providing DC offset
• Digital to Analog Converters
• Audio Mixer

Non-Inverting Summing Amplifier

Fig.3 Non-Inverting Summing Amplifier

Fig.3 Shows the non-inverting summing amplifier. Where the two inputs V1 and V2 are applied to the non-inverting op-amp terminal through resistor R₁ and R₂.

The output of the op-amp can be given as

Proof:

The output can be found by applying the superposition theorem. To find the output, let’s consider only one input at a time. If V₁ is acting alone and V₂ = 0 (as shown in fig.4), then voltage V₁+ at the non-inverting input is

Fig. 4 Non-Inverting Summing Amplifier (When V₂ = 0)

Similarly, as shown in Fig.5, when voltage V1 = 0 and V2 is acting alone then voltage V₂+ can be given as

Fig.5 Non-Inverting Summing Amplifier (When V₁ = 0)

Considering both inputs simultaneously, the total voltage at the non-inverting input terminal

That means overall output voltage of the op-amp is

When R₁ = R₂ = R then output of the op-amp

And when R_f = R_a then output

For more information about inverting and non-inverting summing amplifier, please check this video:

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Fig. 1 shows the non-inverting configuration of the op-amp. In this configuration, the input is applied at the non-inverting terminal of the op-amp.

Fig. 1 Non-Inverting op-amp Configuration

In this configuration, there is a negative feedback from the output to the input side. As shown in Fig.2, the fraction of output voltage is given as feedback to the input side. Due to this negative feedback, the op-amp operates in the linear region. In this configuration, the output of the op-amp can be as Vo = ( 1 + Rf / R1) Vin

Fig.2. Negative Voltage Feedback in the Non-Inverting op-amp configuration

Derivation of Closed Loop Voltage Gain of the non-inverting op-amp Configuration

Here, it has been assumed that the op-amp is ideal op-amp, and no current is flowing into the op-amp terminals. As shown in figure 2, the fraction of output voltage (Vx) is given as feedback to the input.

Vx = R1x Vo / (R1 + Rf)

Since, op-amp is operating in the linear region, the concept of virtual ground / virtual short is valid.That means the voltage at the inverting and the non-inverting input terminals will be the same. (V+ = V-)

Here, V+ = Vin and V- = Vx. That means Vin = Vx = R1 x Vo / (R1 + Rf)

Vo = ( 1 + Rf/ R1) x Vin

As, per the equation, in the case of the non-inverting op-amp, the output signal is in phase with the input signal. Moreover, the input impedance of the non-inverting op-amp is very high compared to inverting op-amp. (Ideally, it is infinite, because, for the ideal op-amp, no current is flowing into the op-amp terminal) And because of the high input impedance, the op-amp can be used as a buffer in many applications.

Op-amp as a Buffer

As shown in figure 3, the op-amp is used as a buffer. In the non-inverting configuration, If Rf = 0 and R1 = ∞ then it will act as a buffer.

Fig.3 Op-Amp as Buffer

When op-amp is used as a buffer, then it provides very high input impedance and low output impedance. Also, since op-amp is used with the negative feedback ( in the linear region), the voltage at the inverting and non-inverting terminal will be same. (V+ = V-)

And for the buffer circuit, Vo = Vin. That means the output of the op-amp follows the input signal. In this configuration, the gain of the op-amp is unity. And that’s why it is also known as unity follower.

Because of the high input impedance and low output impedance, the buffer can isolate the two stages of the circuit and at the same time, it can provide the output of the one circuit as an input to other circuit. (As shown in the figure 4). It is particular useful, when there is a impedance mismatch between the two stages.

Figure 4. Op-Amp as a buffer can be used to isolate the two circuits

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As discussed in the previous article, the op-amp is a very high gain differential amplifier. In the open-loop configuration, the typical gain of the op-amp is 10⁵ to 10⁶ 

Fig. Operational Amplifier

Because of high open-loop gain, even for a small differential input between the two terminals, the output of the op-amp will get saturated.

Fig. Voltage Transfer Curve of Operational Amplifier

To use the op-amp as an amplifier, it needs to be operated in the linear region. In the open-loop configuration, the linear input range is very limited. For example, if the saturation voltage of the op-amp is ±10V and open-loop gain is 10⁶ then the differential input range over which the op-amp will operate in the linear range is limited to ± 10 μV. (Saturation Voltage / open-loop gain).

To use the op-amp as an amplifier over a wider input range, somehow its gain needs to be controlled. It is possible to control the gain of the op-amp with negative feedback.

As shown in the figure, in the inverting op-amp configuration, a fraction of output is feedback towards the input side using the feedback resistor Rf and the input is applied at the inverting input terminal through resistor R1.

Fig. Inverting op-amp configuraiton

In this configuration, it is possible to control the gain of the op-amp using feedback resistor Rf and resistor R1.

Concept of Virtual Ground in Operational Amplifier

Ideally, the concept of the virtual ground is applicable when the op-amp is ideal and it is used in the linear range with negative feedback. But for practical op-amps also, since the open-loop gain of the op-amp is very high (10⁵ to 10⁶), this concept is still applicable.

According to this concept, when the op-amp is operated with negative feedback (in the linear region), both inverting and non-inverting op-amp terminals will be at the same potential. When non-inverting op-amp terminal is grounded then the inverting terminal will also act as gound. Although the inverting terminal is not actually grounded, it acts as a virtual ground.

Let’ understand the concept of virtual ground with inverting op-amp configuration.

With negative feedback, assuming op-amp is operating in the linear region, the output of the op-amp can be given as

Vo = Ao x (V+ – V-) = Ao x Vd

V+ is the voltage at the non-inverting input terminal

V- is the voltage at the inverting input terminal

Ao – Open loop gain of the op-amp

For one practical op-amp, let’s say the open-loop gain of the op-amp is 10⁶  and with negative feedback output voltage is 10V.

∴ Vd = 10V / 10⁶ = 10 μV

∴ V+ – V- = 10 μV

with the negative feedback, the voltage difference between the two op-amp terminals is merely 10 μV. 

For ideal op-amp, if the open-loop gain is considered as infinite then Vd = 0 or V+ = V- 

It shows that when the ideal op-amp is operated with negative feedback, both inverting and non-inverting terminals will be at the same potential. If a non-inverting op-amp terminal is grounded then the inverting terminal will also act as a virtual ground.

Op-Amp output in inverting configuration (and derivation)

Fig. Inverting op-amp configuration

For deriving the output of the op-amp, first, let’s consider the op-amp is ideal. For the ideal op-amp, the input impedance is infinite and no current is flowing into op-amp terminals.

And with the negative feedback, the concept of virtual ground can be applied. Since the non-inverting terminal is at the ground potential, the inverting terminal will also act as a virtual ground. (The voltage at node A will be zero)

Applying KCL at node A, 

I1 = I2 

⇒ (Vin – VA)/ R1 = (VA – Vo)/Rf

Since VA = , Vin /R = -Vo /Rf

⇒ Vo = -(Rf / R1)*Vin

As per the expression, by controlling the feedback resistor and resistor R1, it is possible to control the gain of the op-amp. Moreover, there is a negative sign in the output expression. 

e.g if the input is 1V DC and gain of the op-amp is 5, then the output of the op-amp in the inverting configuration is -5V. 

In the next article, the non-inverting op-amp configuration will be discussed. 

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As its name suggests, the Operational Amplifier is one type of amplifier. The basic function of any amplifier is to amplify the input signal. But apart from amplifying the signal, it is also possible to perform different arithmetic operations using op-amp.

In the early days, when digital computers were not evolved, then op-amp was used to perform the different arithmetic operations like addition, subtraction, integration, and differentiation.

That’s the reason it is known as the Operational Amplifier. (An amplifier, which can perform different (arithmetic) operations)

The Circuit Symbol of Op-Amp

Fig. 1 The circuit symbol of an Operational Amplifier

As shown in the figure, the op-amp consists of two inputs, one output, and two power supplies. (positive and negative power supplies).

Some operational amplifiers work on the single power supply. (Such op-amps are known as single supply op-amp)

In the op-amp circuit symbol, the input terminal marked as positive is known as a non-inverting input terminal, and the terminal marked with a negative sign is known as the inverting input terminal. (as shown below in the figure)

V+ is the positive biasing voltage

V- is the negative biasing voltage

Fig.2  Inverting and non-inverting input terminals of the op-amp

Operation of Op-Amp in the open-loop configuration:

In the open-loop configuration, the op-amp is operated without any kind of feedback.

In the open-loop configuration, the op-amp amplifies the difference between the two input terminals (Between inverting and non-inverting inputs)

As shown in the fig.1, if V1 and V2 are the inputs at non-inverting and the inverting input terminals, then the output of the op-amp

Vo = Aol x (V1 – V2)

where Aol –  open-loop gain of the op-amp

As shown in Fig.3, if the input is applied at the non-inverting input terminal (V1) and another input  terminal is grounded then the output can be given as

Vo = Aol x V1

Fig. 3 Operation of the op-amp in open-loop configuration with the input applied at the non-inverting input terminal

Similarly, as shown in Fig. 4 when the input is applied only at the inverting input terminal and non-inverting input is grounded then the output can be given as

Vo = – Aol x V2

Fig. 4 Operation of the op-amp in open-loop configuration with the input applied at the inverting input terminal

If the differential input Vd is applied between the non-inverting and the inverting input terminal (as shown in fig. 5), then output in the open-loop configuration can be given as

Vo = Aol x Vd 

Fig. 5 Operation of the op-amp in the open-loop configuration with differential input

Typically, the open-loop gain of the op-amp is very high. (In the range of 10^5 to 10^6).

Even for very small differential input, the output of the op-amp will get saturated.

Example: 

if Vd = 1mV and Aol = 10^5, then Vo = 100V. (Theoretically)

But the output of the op-amp will be limited to positive and the negative saturation voltage (± Vsat).

For one op-amp, if the saturation voltages are ±12V, then for the above example, the output will be restricted to 12V,

And even for Vd = 5mV, Vo = 12V.

So, in such a case, it is said that the op-amp is operating in the saturation region. Typically the saturation voltage is less than the biasing voltages of the op-amp.

Voltage transfer curve of the op-amp in open loop configuration:

The same phenomenon explained above can also be explained with the help of the Voltage transfer curve of the op-amp.

Fig. 6 shows the voltage-transfer curve of the op-amp in the open-loop configuration.

Fig. 6 Voltage transfer curve of the op-amp in the open-loop configuration

As shown in the figure, the output voltage Vo is represented in the Y-axis and differential input to the op-amp is represented on the X-axis.

It is evident that, in the open-loop configuration,  for very small differential input only (typically in μV) the output of the op-amp will operate in the linear range. Beyond that, the op-amp will operate in the saturation region. (Because of the very high gain of the op-amp). In the linear region, the slope of the curve represents the open-loop voltage gain of the op-amp.

In the open-loop configuration, the op-amp can be used as a comparator. Apart from that, with the feedback, the op-amp can be used in various applications.

Here is the few important applications of the op-amp.

Applications of the Operational Amplifier:

1. Comparator
2. Active Filters
3. Oscillators and Multivibrators
4. Waveshaping and Waveform generating circuits
5. Analog to Digital Converter (ADC)
6. Digital to Analog Converter (DAC)
7. Linear Amplification
8. To perform the arithmetic operation on the signal (Addition, Subtraction, Multiplication, Integration, Differentiation etc.)

Equivalent Circuit of the Operational Amplifier:

Fig. 7 Equivalent circuit of the operational Amplifier

Fig. 7 shows the equivalent circuit of the op-amp.

Where,

V1, V2 – Non-inverting and inverting input of the op-amp

Vd = V1 – V2

Ri – Input resistance of the op-amp

Ro – Output Resistance of the op-amp

A- Open loop gain of the op-amp

Characteristics of Ideal Op-Amp: 

As, mentioned above, the op-amp is a very versatile IC and can be used in various applications. Because of its favorable characteristics, it is used in various applications.

Here is the list of characteristics of the ideal op-amp

1.  Infinite Input Impedance
2.  Zero Output Impedance
3.  Infinite Voltage Gain
4.  Infinite Bandwidth
5.  Infinite Slew Rate
6. Infinite Common Mode Rejection Ratio (CMRR )
7.  Zero input offset voltage (Output is Zero when input is Zero)

The characteristics of the actual op-amp will be different from the ideal op-amp. To get an idea, the characteristics of the very popular op-amp IC 741 is shown below:

Table 1: Characteristics of op-amp IC 741

To get more information about op-amp, check this video on Operational Amplifier .

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