Lab – 2 op-amp Circuits Experiment – 2.1 Basic op-amp circuits Experiment – 2.2 Non-linear op-amp circuits Basic op-amp circuits 02.1.1 Objective 1. To sketch the following basic op-amp circuits and explain the operation of each: (a) Inverting amplifier (b) Non-inverting amplifier (c) Voltage follower (d) Differential amplifier (e) Summing amplifier (f) Integrator and differentiator. 2. To analyze and design circuits of the type listed in item I above for input & output impedances, voltage gain and bandwidth. 3. To trouble shoot and analyze faults in the op-amp circuits. 2.1.2 Hardware required a. Power supply b. Equipments c. Resistors d. Capacitors e. Semiconductors f. Miscellaneous

– – -

variable regulated low voltage dc source AFO, CRO, DMM

IC 741 op-amp Bread board and wires

2.1.3 Pre Lab questions 1) Identify each of the op-amp configurations

2) A nn-inverting amplifier has R1 of 1K of 100K. Determine Vf and  (Feedback voltage and feedback fraction), if Vo = 5V 3) For the amplifier in Fig. (b) Determine the following (a) ACL (NI) (b) Vo (c) Vf 4) Find the value of RF that will produce closed-loop gain of 300 in each amplifier in fig(c)

5) Determine the approximate values for each of the following quantities in Fig (d).

6) If a signal voltage of 10mV rms is applied to each amplifier in Fig(e), What are the o/p voltage?

7) Determine the input and output impedances for each amplifier configuration, (Zin=10M, Zo=75, AOL = 175,000). in fig(f)

8) Determine the BW of each of the amplifiers in Fig. The op-amps have an open-loop gain of 90dB and a unity gain bound width of 2MHz.

9) Determine the o/p voltage of each amplifier in Fig (h).

2.1.4 Theory In this laboratory experiment, you will learn several basic ways in which an op-amp can be connected using –ve feedback to stabilize the gain and increase the frequency response. The extremely high open-loop gain of an op-amp creates an unstable situation because a small noise voltage on the input can be amplified to a point where the amplifier in driven out of its linear region. Also unwanted oscillations can occur. In addition, the open-loop gain parameter of an op-amp can vary greatly from one device to the next. Negative feedback takes a portion of o/p and applies it back out of phase with the input, creating an effective reduction in gain. This closed-loop gain is usually much less than the open-loop gain and independent of it. 2.1.4.1 Closed – loop voltage gain, ACL The closed-loop voltage gain is the voltage gain of an op-amp with external feedback. The amplifier configuration consists of the op-amp and an external –ve feedback circuit that connects the o/p to the inverting input. The closed loop voltage gain is determined by the external component values and can be precisely controlled by them. 2.1.4.2 Non-inverting amplifier An op-amp connected in a closed-loop configuration as a non-inverting amplifier with a controlled amount of voltage gain is shown in Fig 3-1-1.

The input signal is applied to the non-inverting (+) input The output is applied back to the inverting (-) input through the feedback circuit (closed loop) formed by the input resistor R1 and the feedback resistor Rf. This creates –ve feedback as follows. Resistors R1 and Rf form a voltage-divider circuit, which reduces Vo and connects the reduced voltage Vf to the inverting input. The feedback is expressed as R1 Vf  ( )Vo R1  R f The difference of the input voltage, Vin and the feedback voltage, Vf is the differential input of the opamp. This differential voltage ins amplified by the gain of the op-amp and produces an o/p voltage expressed as  Rf  Vin Vo  1  R1   The closed-loop gain of the non-inverting amplifier is, thus ACL(NI) =

1

Rf R1

Notice that the closed loop gain is * independent of open-loop gain of op-amp * set by selecting values of RI and Rf An expression for the input impedance of a non-inverting amplifier can be written as

Where

(1  AOL  ) Z IN Zin(NI) = AOL = open-loop voltage gain of op-amp ZIN = internal i/p impedance of op-amp (without feedback)  = attenuation of the feedback circuit Vf R1  = Vo R1  R f

Eq. (1-2-3) shows that the input impedance of the non-inverting amplifier configuration with –ve feedback is much greater than the internal o/p impedance of the op-amp itself. The o/p impedance of a NI amplifier can be written as Zo Z o ( NI )  1  AOL This eq. shows that the o/p impedance of NI amplifier is much less than the internal o/p impedance, Zo of the op-amp. 2.1.4.3 Voltage follower The voltage follower configuration is a special case of the non-inverting amplifier where all the o/p voltage is feedback to the inverting input by straight connection, as shown in fig. 2-1-2.

As you can see, the straight feedback connection has a voltage gain of (which means there is no gain). ACL (VF) = 1 The most important features of the voltage follower configuration are its very high input impedance and its very low output impedance. These features make it a nearly ideal buffer amplifier for interfacing high-impedance sources and low-impedance loads. Z IN (VF )  (1  Aol ) Z IN

Z O (VF ) 

ZO 1  AOL

As you can see, the voltage follower input impedance is greater for a given AOL and ZIN than for the non-inverting amplifier. Also, its o/p impedance is much smaller. 2.1.4.4 Inverting amplifier An op-amp connected as an inverting amplifier with a controlled amount of voltage gain is shown in fig. 2-1-3.

The i/p signal is applied through a series i/p resistor R1 to the inverting input. Also, the o/p is fed back through Rf to the same input. The non-inverting i/p is grounded. An expression for the o/p voltage of the inverting amplifier is written as Rf Vo   VIN R1 The –ve sign indicates inversion. The closed-loop gain of the inverting amplifier is, thus ACL ( I )  

Rf

R1 The i/p & o/p impedances of an inverting amplifier are Zin(I) = Ri Zo(I) =

Zo 1  AOL

The o/p impedance of both the non-inverting and inverting amplifier configurations is very low; in fact, it is almost zero in practical cases. Because of this near zero output impedance, any load impedance connected to the op-amp o/p can vary greatly and not change the o/p voltage at all. 2.1.4.5 Summing amplifer The summing amplifier is an application of the inverting op-amp configuration. The summing amplifier has two or more inputs, and its output age is proportional to the algebraic sum of its input voltages. Fig. 2-1-4 shows a two-input inverting summing amplifier. Case-1:If all the three resistors are equal (R1=R2=Rf=R) then Vo = - (Vinl + VINZ) The above equation shows that the o/p voltage has the same magnitude as the sum of two input voltages but with a –ve sign indicating inversion.

Case-2: when Rf is larger than the input resistors, the amplifier has a gain of value of each equal – value input resistor (R1=R2=R). the general expression Vo  

Rf R

Rf R

, where R is the for the o/p is

(Vin1  Vin 2 )

The above equation shows that the o/p voltage has the same magnitude as the sum of all the input Rf voltages multiplied by a constant determined by the ration . R

Rf Case-3: By setting the ration Rf/R equal to the reciprocal of the number of inputs (n), ie., = R 1 summing amplifier can be made to produce the mathematical average of the input voltages. n

,a

Case-4: A different weight can be assigned to each input of a summing amplifier by simply adjusting the values of the input resistors. In this case, the o/p voltage can be expressed as Vo   (

Rf

Vin1 

Rf

Vin 2 R1 R2 The weight of a particular input is set by the ration of Rf to the resistance Rx for the input (Rx, R1, R2, ….) 2.1.4.6 Subtractor or Differential amplifier The function of a subtractor is to provide an o/p proportional to or equal to the difference of two input signals. A basic differential amplifier or a subtractor circuit is shown in fig. 2-1-5.

The o/p voltage of the differential amplifier can be expressed as R Vo  f (V1  V2 ) R1 Thus it can be seen that the o/p voltage depends on the difference of the input voltages. (V1-V2) can be suitably amplified choosing the values of Rf/R1. The circuit also behaves as a subtractor if Rf=R1.

2.1.4.7 Integrator An op-amp integrator simulates mathematical integration which is basically a summing process that determines the total area under the curve of a function ie., the integrator does integration of the input voltage waveform. Here the input element is resistor and the feedback element is capacitor as shown in fig. 2-1-6.

The o/p voltage is given by t

1 Vsdt  Vc(t  0) Rc o Where Vc (t=0) is the initial voltage on the capacitor. For proper integration, Rc has to be much greater than the time period of the input signal. It can be seen that the gain of the integrator decreases with the increasing frequency so, the integrator circuit does not have any high frequency problem unlike a differentiator circuit. However, at low frequencies such as at dc, the gain becomes infinite. Hence the op-amp saturates (ie., the capacitor is fully charged and it behaves like an open circuit). In order to limit the gain of the integrator at low frequencies, usually the feedback capacitor is shunted by a resistance Rf, and hence saturation problems can be avoided. A practical integrator circuit is shown in Fig. 2-1-7. Vo  

2.1.4.8 Differentiator An op-amp differentiator simulates mathematical differentiation, which is a process of determining the instantaneous rate of change of a function. Differentiator performs the reverse of integration function. The o/p waveform is derivative of the i/p waveform. Here, the input element is a capacitor and the feedback element is a resistor. An ideal differentiation is shown in fig. 2-1-8.

The o/p voltage is given by Vo   Rc (

dVs ) dt

For proper differentiation, Rc has to be much smaller than the time period of the input signal. It can be seen that at high frequencies a differentiator may become unstable and break into oscillation. Also, the input impedance of the differentiator decreases with increase in frequency, thereby making the circuit sensitive to high frequency noise. So, in order to limit the gain of the differentiator at high frequencies, the input capacitor is connected in series with a resistance R1 and hence autiding high frequency noise and stability problems. A practical differentiator circuit is shown in fig. 2-9-1.

2.1.5 Troubleshooting As a technicial, you may encounter situations in which an op-amp or its associated circuitry has malfunctioned. The op-amp is a complex IC with many types of internal failures possible. However, since you cannot trouble shoot the op-amp internally, you can treal it as a single device with only a few connections to it. If it fails, you replace it just as you would a resistor, capacitor, or transistor. 2.1.5.1 Faults in the non-inverting amplifier. The first thing to do when you suspect a faulty circuit is to check for the proper supply voltage and ground. Having done that, several other possible faults are as follows. Open feedback resistor: If the feedback resistor, Rf in Fig. 3-1-1 opens, the op-amp is operating with its very high open-loop gain, which causes the input signal to drive the device into non-linear operation and result in a severely clipped o/p signal. Open input resistor: In this case, you still have a closed-loop configuration, But, since R1 is open and effectively equal to , the closed-loop gain from equation 1-2-2 is R R ACL ( NI )  1  f  1  f  1  0  1 R1  This shows that the amplifier acts a voltage follower. You would observe an o/p signal that is same as the input. Internally open non-inverting input: In this situation, because the input voltage is not applied to the opamp the o/p is uro.

Other op-amp faults: In general, an internal failure will result in a loss or distortion of the o/p signal. The best approach is to first make sure that there are no external failures or faulty conditions. If everything else is good, then the op-amp must be bad. 2.1.4.2 Faults in the voltage follower The voltage follower is a special case of the non-inverting amplifier. Except for a bad op-amp, a bad external connectietor a problem with the offset null potentiometer, about the only thing that can happen in a voltage follower circuit is an feedback loop. This would have the same effect as an open feedback resistor, as previously discussed. 2.1.5.3 Faults in the inverting amplifier open feedback resistor: In fig. 2-1-3, if Rf opens the i/p signal still feeds though the input resistor and is amplified by the high open-loop gain of the op-amp. This forces the device to be driven into nonlinear operation. This is the same result as in the non-inverting amplifier configuration. Open input resistor: This prevents the i/p signal from getting to the op-amp i/p, so there will be no o/p signal. Failures in the op-amp itself or the offset null potentiometer have the same effects as previously discussed for the non-inverting amplifier configuration. 2.1.5.4 Faults in summing amplifiers If one of the input resistor in a unity-gain summing amplifier opens, the o/p will be less than the normal value by the amount of the voltage applied to the open input. Stated another way, the o/p will be the sum of the remaining input voltages. If the summing amplifier has a non-unity gain, on open input resistor causes the o/p to be less than normal by an amount equal to the gain times the voltage at the open input. 2.1.6 Experiment 1. Non-Inverting amplifier 1.1 Design a non-inverting amplifier for the gain of 15. Let R1=1.5k Assemble the circuit. 1.2 Feed sinusoidal input of amplitude 100mV and frequency 1KHz 1.3 Observe the input voltages and o/p voltage on a CRO. Tabulate the reading in Table 2-1-1. 1.4 Calculate closed-loop gain (ACL), bandwidth (BW), gain-bandwidth product (GBW), input impedance (Zi), and output impedance (Zo). Tabulate the readings in Table 2-1-1. 1.5 Compare the experimental results with the theoretical values. 2. Voltage follower 2.1 Assemble a voltage follower circuit. 2.2 Feed sinusoidal input of amplitude 100mv and frequency 1Khz. 2.3 Observe the input and output voltages on a CRP. Tabulate the readings in Table 2-1-1. 2.4 Calculate ACL, Bw, GBW, Zi and Zo. Tabulate the readings in Table 2-1-1. 2.5 Compare the experimental results with the theoretical values. 3. Inverting amplifier 3.1 Design an inverting amplifier for the gain of 15. Let R1=1.5k. Assemble the circuit. 3.2 Feed sinusoidal input of amplitude 100mv and frequency 1KHz. 3.3 Observe the input and output voltages on a CRO. Tabulate the readings in Table 2-1-1.

3.4 Calculate ACL, Bw, GBW, Zi and Zo. Tabulate the readings in Table 2-1-1. 3.5 Compare the experimental results with the theoretical values. 4. Summing amplifier 4.1 Assemble an adder circuit with Rf =R1=10k and R2=47k. 4.2 Feed sinusoidal input of amplitude 100mv and frequency 1 KHz to each input. 4.3 Observe the input voltages and output voltage on a CRO Find the magnitude of the o/p voltage and tabulate the reading in Table 2-1-2. 4.4 Compare the experimental results with the theoretical values. 5. Differential amplifier 5.1 Assemble a differential amplifier circuit with Rf=R1=10k 5.2 Feed V1=100mv and V2=50mv sinusoidal signal of frequency 1 KHz. To get 2 signals from the same source, use a high resistance potentiometer. 5.3 Observe the i/p and o/p voltages on a CRO. Find the magnitude of the o/p voltage and tabulate the readings in Table 2-1-2. 5.4 Compare the experimental results with the theoretical value. 6. Integrator 6.1 Assemble an integrator circuit with R=1K and C=0.1µf connect Rf of value 1M across the capacitor. 6.2 Feed +IV, 500Hz square wave input. 6.3 Observe the input and output voltages on a CRO. Determine the gain of the circuit and tabulate the readings in table 2-1-3.Model waveform is shown in fig. 2-1-10 6.4 Plot the i/p and o/p voltages on the same scale on a linear graph sheet. 7. Differentiator 7.1 Assemble a differentiator circuit with R=10K and C=0.05µf. Connect a resistor R1 of value 470 between the source and the capacitor. 7.2 Feed + 0.1V, 5 KHz triangular wave input. 7.3 Observe the input and output voltages on a CRO. Determine the gain of the circuit and tabulate the readings in table 2-1-3. Model waveform is shown in fig. 3-1-11. 7.4 Plot the i/p and o/p voltages on the same scale on a linear graph sheet. 2.1.7 Post Lab questions 1. What is the relationship, if any, between the polarity of the output and input voltages in your experimental op-amp? Refer to your data. 2. Can the summer operated as a subtractor? Confirm your answer with the experimental data. 3. Look at Table 2-1-1 and comment on the statement: “The closed-loop gain-bandwidth product is a constant for a given op-amp”. 4. Determine the bandwidth of a non-inverting amplifier, voltage follower and inverting amplifier that were implemented in the laboratory. 5. Determine the gain-bandwidth product of each amplifier. 6. Determine the i/p and o/p impedances of each amplifier. 7. Determine the most likely faults for each of the following symptoms in fig. 2-1-12 with a 100mv signal applied.

(a) No o/p signal (b) o/p severely clipped on both +ve & -ve swings. 8. Determine the effect on the o/p if the circuit in fig. has the following fault (one at a time). (a) o/p pin is shorted to the inverting i/p (b) R3 is open (c) R3 is 10K instead of 910. (d) R1 and R2 are swapped. 9. (a) What is the normal o/p voltage in fig. 2-1-14? (b) What is the o/p voltage of R2 opens? (c) What happens if R5 opens? 2.1.8 Advanced problems 1. Design a non-inverting amplifier with an appropriated closed-loop gain of 150 and a minimum i/p impedance of 100M. 2. Design an inverting amplifier using a 741 op-amp. The voltage gain must be 68 +5% and the input impedance must be approximately 10K. 3. Design a non-inverting amplifier with an upper critical frequency of 10 KHz. 4. Design an inverting amplifier if a midrange voltage gain of 50 and a bandwidth of 20 KHz is required. 5. Design an integrator that will produce an o/p voltage with a slope of 100mv/µs when the i/p voltage is a constant 5v. Specify the input frequency of a square wave with an amplitude of 5v that will result in a 5v peak-to-peak triangular wave o/p. 6. Show the connection of 3-stage amplifiers using 741 op-amp with gains of +10, -18 and -27. Use a 270K feedback resistor for all three stages. What o/p voltage will result for an i/p of 150µv?