OPERATIONAL AMPLIFIERS
By
EXPERIMENT 1: OP AMP CHARACTERISITCS AIM: To determine the following op amp parameters
(1) The input offset voltage (V0s)
(2) The offset current (Ios) and the bias currents (3) Slew rate
(4) The common mode rejection ratio (CMRR)
INTRODUCTION
An operational amplifier (or op-amp in short) is a linear integrated circuit (IC) that has a very high voltage gain; high input impedance and low output impedance. The internal circuit of a very popular op-amp (μA 741) is shown in Fig. 1(a). Its schematic symbol is shown in Fig. 1(b) and its pin diagram in Fig. 1(c).
Fig. 1(b): Schematic symbol for a 741
Fig. 1(c): The 741 chip is shown packaged in an 8-pin dual-in-line package.
As seen from Fig. 1(b), op-amp is provided with two input terminals; Inverting input terminal represented as “ - ” and Non-inverting terminal represented as “ + ”.
The word “inverting” implies that if a signal is applied to the ‘-‘ terminal of the op-amp, it appears with the opposite polarity at the output, i.e., a sinusoidal signal will experience a phase shift of 180°.
The word “non-inverting” implies that if a signal is applied to the ‘+‘ terminal of the op-amp, is amplified without inversion.
The basic circuit consists of a differential amplifier input stage and an emitter follower output stage. The voltage gains of integrated circuit operational amplifiers are extremely high, typically 200 000. Because of this large voltage gain, externally connected resistors must be employed to provide negative feedback for most applications. The op-amp actually amplifies the difference between the voltages applied to its two input terminals.
The two other terminals are provided for the connection of positive and negative power supply voltages. Both polarities are necessary so that the output voltage can vary either side of Zero volts.
The op-amp is a high gain D.C. Coupled amplifier whose closed loop gain can be controlled by a feedback network. It is utilized in a variety of ways to provide solutions to measurement and control problems.
The important op-amp parameters, which are necessary to understand the fundamental concepts of op-amp operation.
Gain: The ideal op-amp would have an infinite open-loop differential gain. The gain is often expressed in decibels (dB). If V1 is the input and V2 is the output-voltage of the op-amp, then gain in decibels.
dB = 20 log10 (V2) / (V1)
Input Resistance: The input resistance of an op-amp is infinitely high. But in practice, the input resistance may be any value between 250 kΩ and 40 MΩ for the op-amps with bipolar transistor input and 1012 fΩ for the op-amps with field-effect transistor (FET) input.
Output Resistance: Basically an op-amp is a voltage amplifier therefore it should have its input resistance as low as possible. Practical op amps have the output resistance of the order of 100 Ω.
Input offset voltage: The output voltage of an op-amp should be zero when the value of an applied voltage at both the input terminals is zero. The input offset voltage of an op-amp is equal to the output voltage for zero input voltage divided by the open-loop voltage gain of the amplifier.
Input offset current: The difference between the bias currents is known as the input offset current. The range of 3-20 nA for bipolar transistor input op-amps and a few pico-amperes (pA) for FET input op-amps.
Input bias current: The input circuit of an op-amp is always a differential amplifier. The input bias current is one-half the sum of the bias currents taken by each input of the op-amp. The input bias current is 10 to 50 nA for a bipolar transistor input op-amp and as low as 10 to 100 pA for the FET input op-amp.
Slew rate: The slew rate of an op-amp is the maximum rate at which its output voltage is capable of changing. It is expressed in volts per second (V/μs). The slew rate for op-amps is in the range of 0.3 – 12 V/μs.
Common-Mode Rejection Ratio (CMRR): The output voltage of an op-amp is Proportional to the voltage applied to the inverting and non-inverting terminals. Ideally when the two voltages are equal, the output voltage should be zero. A signal applied to both the input terminals is called a common-mode signal. It is nearly always an unwanted noise voltage. The ability of an op-amp to suppress common-mode signals is expressed in terms of its common-mode rejection ratio (CMRR). Mathematically, the common-mode rejection ratio is given by the relation,
CMRR = Differential voltage gain Common mode voltage gain Adm /Acm
where
Adm =Differential voltage gain, and Acm =Common-mode voltage gain.
The common-mode rejection ratio can also be expressed in decibels. Thus,
CMRR = 20 log10 (Adm/Acm) dB
Op-amp might have a common- mode rejection ratio of 90 dB. EQUIPMENT
IC op-amp 741 or OP-07 and base; power supply (15-0-15V); multimeter; function generator; CRO; and resistors.
EXPERIMENTAL PROCEDURE
The offset voltage measured using the circuit of Fig. 2.1. Measure the output voltage for different combination of Ri.
Figure 2.1: Offset voltage measurement.
The bias currents and the offset current of the op amp can be measured using the circuit show in the Fig 2.2 under different switch conditions.
Figure 2.2: Measurement of bias currents.
The output voltage S2 open and S1closed is equal to Ib-R while that with S1 open S2 closed is equal to –Ib+R. With both the switches in the open condition, the output voltage V0=IosR. Measure the output voltage under different switch conditions and evaluate Ib-, Ib+ and Ios.
Wire the circuit as show in the Fig 2.3 for measurement of the slew rate. Fix the frequency of input signal vi at a convenient value, say f=5kHz. Increase the amplitude of the input signal until distortion of the output signal. If Vp is the peak value of the output voltage, the slew rate is equal to 2πfVp. Repeat the experiment at different frequencies. Show that fVp is constant.
It is rather difficult to detect the onset of a small amount of distortion in the output signal. As an alternative distortion of the input error signal at the summing point may be observed. Use of a distortion meter facilitates accurate determination of the slew rate.
Fig. 2.4 illustrates the technique of measuring the CMRR of an op-amp. If the resistances are matched well, the signal at the input is essentially the common-mode signal, i.e., Vs = Vc and Ac = Vo / Vc. However, due to imbalance of the amplifier there will be an output voltage Vo = Ad Vi. Then
CMRR = Ad / Ac --- (1)
[(R1+R2) / R1] Vs / Vo (R2 >> R1)
Figure 2.4: Measurement of CMRR.
Keep R1 = 100 Ω and R2 = 100 kΩ and measure Vo for a particular value of Vs. Evaluate CMRR using the equation (1). Vary the amplitude of Vs and determine CMRR. Study how CMRR varies with the amplitude of the common-mode signal.
TYPICAL PARAMETERS IC OPERATIONAL AMPLIFIER
S.No Parameter Symbol Value
1 Input offset voltage Vos 2 mV
2 Input offset current Ios 10 nA
3 Input bias current IB 100 nA
4 Input offset temperature drift - 5 μV / °C 5 Input offset current temperature drift - 10 nA / °C 6 Open loop d.c. Voltage gain AVOL 100, 000 7 Open loop 3db bandwidth BWVOL 5 kHz
8 Unity gain bandwidth ft 0.5 MHz
9 Slew rate Sr 1 V /μs
10 Differential input impedance Ri 100 KΩ 11 Common mode input impedance Rc 100 MΩ
12 Output impedance Ro 50 Ω
EXPERIMENT 2: OP AMP CONFIGURATIONS AIM: To study the following op amp configurations
(1) Inverting amplifier (2) Non-inverting amplifier (3) Differential amplifier (4) Voltage follower (5) Current follower INTRODUCTION
The IC op-amp is a versatile system building block and is being used in automatic control systems, sound systems, communication systems and instrumentation. The op-amp never used without the application of negative or positive feedback. There are two ways in which an op-amp can be connected to act as an amplifier; one method gives an inverting gain and the other gives a non-inverting gain. The method of connecting the op-amp which produces inverting gain is called inverting amplifier. Similarly, the method of connecting the op-amp which produces non-inverting gain is called non-inverting amplifier.
EQUIPMENT
IC op-amp 741 or OP-07 and base; Dual power supply (15-0-15V); multimeter; function generator; CRO; variable D.C. source (steps of 0.2 V); and phototransistor.
EXPERIMENTAL PROCEDURE INVERTING AMPLIFIER
Figure 1 shows the circuit diagram for inverting amplifier makes use of a single resistor (R1) and a single feedback resistor (R2). The resistor (R1) is connected between the input terminal of the amplifier circuit and inverting input terminal (-) of the op-amp. The resistor (R2) is connected between the inverting input terminal (-) and the output terminal of the op-amp. The non-inverting terminal (+) is connected to the ground. The inverting amplifier produces a 180° phase shift in voltage from input to output. Thus the input and output signals of the inverting amplifier are not in-phase with each other.
Figure 1: Circuit diagram for inverting amplifier.
The op-amp gain without any feedback (called open-loop gain) is very high. This means that the voltage at the inverting (i.e., ‘-‘) terminal must be very small. As a matter of fact, the input voltage at the inverting terminal will be very nearly at the same potential as the non-inverting terminal. Now since the non-inverting input is grounded, the inverting input of an op-amp is also at the ground potential and is referred to as virtual ground.
The equation for inverting amplifier is
Vout = -(R2/R1) Vin Or
Vout = -Av Vin where Av = R2 / R1 Vout = - (R2 / R1) Vin
The negative sign indicates that the inverting amplifier output is 180° out of phase with respect to the input.
The open-loop and closed-loop gain: The open-loop voltage gain (AOL) of an op-amp is
the gain that is measured when there is no feedback path (i.e., no physical connection) between the output and input circuit. When a feedback path is present, such as the R2 connection in the inverting amplifier, the resulting circuit gain is referred to as the closed-loop gain (ACL).
Input resistance (Rin): The op-amp has an extremely high input resistance (ideally
infinite) yet the inverting amplifier does not have that high value. The value of R1 will always be much less than the input resistance of the op-amp, therefore, the overall input resistance of an inverting amplifier will be much lower then the op-amp input resistance.
Output resistance: The output resistance of an op-amp is usually very low (of the order
of 100 Ω), the presence of R2 reduces the overall output resistance of the inverting amplifier below 100 Ω.
Common-mode rejection ratio: CMRR of the inverting amplifier will be much lower
than that of the op-amp. Mathematically, CMRR of the inverting amplifier is, CMRR = ACL / ACM
where
ACL = The closed loop voltage gain of the inverting amplifier ACM = The common-mode gain of the op-amp
NON-INVERTING AMPLIFIER
Figure 2 shows the circuit diagram for non-inverting amplifier makes use that the input
signal is applied to the non-inverting op-amp input and the resistor R1 is returned to
ground.
Figure 2: Circuit diagram for non-inverting amplifier.
Voltage gain: The op-amp gain without feedback (called open-loop gain) is very high.
This means that voltage at the inverting terminal should nearly be the same as that at the non-inverting terminal. Since the non-inverting input is at a potential of Vin, therefore inverting input is also at the same potential.
The amplifier voltage gain,
Av = Output voltage / Input voltage Vo / Vin
or 1 + R2 / R1 Vo = (1+R2 / R1) Vin
The voltage gain of a non-inverting amplifier will always be greater than the equivalent gain of the inverting amplifier by a value of 1.
Input resistance: The non-inverting amplifier has extremely high input resistance
because the input signal is applied directly to the op-amp (i.e., not through a resistor R1 as it happens in the case of inverting amplifier). The presence of feedback network causes the amplifier input resistance to be greater than the input resistance of the op-amp.
Output resistance: The output resistance of the non-inverting amplifier is lower than the
output resistance of the op-amp.
Common-mode rejection ratio: CMRR of the non-inverting amplifier will be much
lower than that of the op-amp. Mathematically, CMRR of the inverting amplifier is, CMRR = ACL / ACM
where
ACL = The closed loop voltage gain of the inverting amplifier ACM = The common-mode gain of the op-amp.
Non-inverting amplifier as a buffer: The extremely high input resistance and extremely
low output resistance of the non-inverting amplifier makes it very useful as a buffer. The emitter follower and source follower are circuits that can be used to match a source with high input resistance to a load with low resistance. The non-inverting amplifier can be used for the same purpose.
DIFFERENTIAL AMPLIFIER
Figure 3 shows the circuit diagram for differential amplifier makes use that the voltages are applied at both the op-amp inputs (inverting and non-inverting inputs) through the resistors. And the difference between these two voltages is amplified. But the open-loop voltage gain of most op-amps is just too great to be used without feedback. So, like other op-amp circuits, a practical difference amplifier must have negative feedback.
Figure 3: Circuit diagram for differential amplifier. The voltage gain of the circuit is
Av = Vout / (V1 – V2) = R2 / R1 Vout = R2 / R1 (V2 – V1)
VOLTAGE FOLLOWER
Figure 4 shows the circuit diagram for voltage follower makes use that the input voltage is applied at the non-inverting input of an op-amp, and the inverting input is connected to the op-amp output. Because of the direct connection between the inverting input and output terminals, a 100 % voltage-series feedback is applied. The equation of a voltage follower is,
Vout = Vin
Figure 4:Circuit diagram for voltage follower.
The voltage follower has a very high input resistance and a very low output resistance. The main application of a voltage follower is as a means of connecting a source with high input resistance to a load with low output resistance, i.e., to act as a buffer amplifier. The common-mode rejection ratio (CMRR) of a voltage follower circuit is given by the relation,
CMRR = ACL / ACM where
ACL = The closed loop voltage gain of the inverting amplifier ACM = The common-mode gain of the op-amp.
Since the closed loop gain (ACL) is equal to ‘1’, therefore, the common-mode rejection ratio,
CURRENT FOLLOWER
Figure 5 shows the circuit diagram for current follower makes use that provides an output voltage that is directly proportional to input current. The op-amp connected in the inverting configuration and R1 = 0.
Figure 5: The circuit diagram for current follower.
The op-amp input current id is essentially zero; the input current directly flows through Rf. Since V- terminal is a virtual ground, the output voltage is
Vo = - in Rf
The input impedance of current follower is approximately zero since V- terminal is virtual ground. The input impedance is Rf / AVOL. The output impedance is quite small since R1 = 0.
Example:
Use the current follower to measure the current of an optoelectronic device like phototransistor as a function of the intensity of light using the circuit as shown in Figure 6.
EXPERIMENT 3: OP AMP CIRCUITS USED IN INSTRUMENTATION AIM: To study the following op amp circuits used in instrumentation
(1) Inverter (2) Adder (3) Subtractor (4) Multiplier (5) Division (6) Integrator (7) Differentiator
(8) Voltage to current converter
INTRODUCTION
An op-amp can be used as a constant gain amplifier, voltage-summing amplifier, voltage buffer amplifier, basic amplifier in instrumentation circuits, comparator, in oscillator circuits and active filters.
EQUIPMENT
IC op-amp 741 or OP-07 and base; Dual power supply (15-0-15V); multimeter; function generator; CRO; variable D.C. source (steps of 0.2 V); and phototransistor.
EXPERIMENTAL PROCEDURE INVERTER
The circuit of an operational amplifier used as an inverter is shown in Figure 1. The feedback resistance Rf is made to the resistance, R1 is connected to the inverting end of the amplifier.
The output voltage is
V0 = - (Rf /R1) Vin
V0 = - Vin (since Rf = R1)
Figure 1: The circuit diagram for inverter.
ADDER OR SUMMING AMPLIFIER
The summing amplifier is an op-amp circuit that accepts several inputs and provides an output that is proportional to the sum of inputs. The circuit of an operational amplifier used as an adder or summing amplifier is shown in Figure 2. The circuit that performs the addition of signals with amplification using the superposition theorem, the output voltage is
V0 = - [(Rf / R1) V1 + (Rf / R2) V2 + (Rf / R3) V3]
Figure 2: The circuit diagram for adder or summing amplifier.
The input signals can be added together with different factors. All the resistors are chosen to be equal; the circuit acts as a pure adder and adds the input voltages together at the output i.e., R1 = R2 = R3 = Rf the circuit acts as a pure adder and output voltage is
V0 = -(V1+V2+V3) i.e., sum of the individual input voltages.
A summing amplifier can be used to produce the mathematical average of input voltages. This is obtained by setting the ratio of the feedback resistor to the input resistor equal to the reciprocal of the number of inputs. This is because of the reason that the average of several numbers is obtained by adding the numbers and then dividing the quantity of numbers. Such a summing amplifier is known as an averaging amplifier.
SUBTRACTOR
The Subtractor is an op-amp circuit that accepts two inputs and provides an output that is proportional to the subtraction of inputs. The circuit of an operational amplifier used as a Subtractor is shown in Figure 3. The output of the Subtractor circuit is
V0 = -[-V1 (Rf / R1 * Rf / R3) + V2 (Rf / R2)]
Figure 3: The circuit diagram for Subtractor.
If Rf = R1 = R2 = R3, the circuit acts as a pure Subtractor, with the output V0 = V1 – V2
MULTIPLIER
The multiplier is an op-amp circuit that accepts one input and provides an output that is proportional to the multiplication of input with feedback resistor. The multiplication is depends only on feedback resistor. The circuit of an operational amplifier used as a multiplier is shown in Figure 4. The output voltage of an op-amp in the inverting mode is
V0 = -(Rf /R1) V1
Figure 4: The circuit diagram for multiplier If Rf >R1, the circuit acts as a multiplier
DIVIDER
The divider is an op-amp circuit that accepts one input and provides an output that is proportional to the division of input with feedback resistor. The division is depends only on feedback resistor. The circuit of an operational amplifier used as a divider is shown in Figure 5. The output voltage of an op-amp in the inverting mode is
V0 = -(Rf /R1) V1
Figure 5: The circuit diagram for divider If Rf <R1, the circuit acts as a divider INTEGRATOR
The integrator is a circuit whose output is proportional to the area of its input waveform. The circuit of an operational amplifier used as an integrator is shown in Figure 6. The RC circuit itself also acts as a simple integrator. But the problem with such a simple circuit is that the output voltage is not a linear triangular output as it should be. The function of the op-amp is to linearize the output.
Figure 6: The circuit diagram for integrator.
The inverting input to the op-amp is held at a virtual ground by the differential amplifier in the op-amp input circuit. Therefore the input current, I1 = Vin / R1. Because of the high input impedance of the op-amp, virtually all of I1 will flow to the capacitor. The output
voltage is proportional to the integral of the input voltage. Using kirchoff’s current law at node V-,
in = Ic or
(V- - V1) / R = C d/dt (V0 – V-) For infinite differential gains,
V- = 0 Therefore - V1 / R = C d/dt V0 By integration,
V0 = - 1/RC ∫ V1 dt
Vin is constant for a given period of time R1 and is a fixed value, I1 can also be assumed to be a constant value. Since virtually all of I1 flows to the capacitor, C1 is being charged by a constant current source. Thus as long as Vin is constant, the capacitor will charge/discharge at a linear rate. This produces a linear ramp output as shown in Figure 6(a).
From the figure 6(a) that when the input goes positive (i.e., from –V to +V), the output is a negative ramp. When the input goes negative (i.e., from +V to –V), the output is a positive ramp. This indicates that the circuit output is 180° out of phase with the input. DIFFERENTIATOR
The differentiator is a circuit whose output is proportional to the rate of change of its input signal. The circuit of an operational amplifier used as a differentiator is shown in Figure 7. The position of a capacitor and resistor is reversed in a differentiator in comparison to the integrator.
Figure 7: The circuit diagram for differentiator. Using kirchoff’s current law at node V-,
C d/dt (V- - V1) = (V0 – V-) / R V- = 0 Therefore - C d/dt (V1) = V0 / R or V0 = -RC d/dt (V1)
The input signal for the differentiator is triangular waveform. The resulting output is a square waveform. The operational amplifiers are normally not used as differentiator as they tend to decrease the signal to noise (S/N) ratio. Therefore the ratio of signal to noise voltage at the output terminal of the op-amp is 2/0.3 = 6.67. Hence, the noise level at the output increases immensely. There is a limit on the high frequency operation of the differentiation. The circuit will start to lose its operating characteristics at one-tenth the value of frequency.
VOLTAGE TO CURRENT CONVERTER
The circuit diagram for voltage to current converter is shown in Figure 8. Since differential voltage is quite small, the input voltage V1 is applied directly across R1 and hence
iR1 = V1 / R1
Figure 8: The circuit diagram for voltage to current converter.
However this current must be supplied by the output of op-amp. Therefore, iL = iR1
Thus the circuit acts as voltage to current converter. It is clear that the current through RL is independent of resistance RL. Hence, this circuit can be used as constant current source controlled by voltage. The input impedance is quite large.
