24.1 OPERATIONAL AMPLIFIERS
24.1.1 Introduction
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| Figure 24.1 The figure shows the external appearance of an op-amp packaged as an integrated circuit, containing numerous transistors and resistors fabricated on a silicon chip. |
1. The operational amplifier, or op-amp, is a differential amplifier which has very high gains.
2. Its circuit is composed of a large number of transistors and resistors. All these components are assembled together in the form of an integrated circuit, which is fabricated on a silicon chip. Figure 24.1 shows an external view of one such packaged chip.
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| Figure 24.2 741 Operational Amplifier (Op-Amp) |
3. One op-amp which is quite widely used is the 741 op-amp.
4. The amplifier can be used as:
- (a) an inverting amplifier
- (b) a non-inverting amplifier
- (c) a voltage comparator
- (d) an integrator
- (e) an oscillator
24.1.2 Symbol for Op-amp and Connections
1. Symbol
Figure 24.3 shows a schematic diagram representing ani op-amp.
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| Figure 24.3 The figure shows the schematic symbol of an operational amplifier with its input and output terminals. |
2. Connections
An op-amp has several terminals which are used for connecting the amplifier to the external components. Some of the terminals drawn in a diagram of an op-amp are as follows:
(a) Two input terminals
A voltage of V1 is applied to an input of the non-inverting amplifier (marked with a ‘+’ sign).
A voltage of V2 is applied to the input of the inverting amplifier (marked with a ‘−’ sign).
(b) An output terminal
The resultant voltage appears as an output voltage Vo.
(c) Two terminals for external power supply
There is one terminal for positive supply voltage +Vs.
There is another one for negative supply voltage −Vs.
24.1.3 Supply Voltages
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| Figure 24.4 The figure shows how positive and negative external voltage supplies are connected to an operational amplifier. |
Figure 24.4 is a schematic diagram showing how two external voltage supplies are connected to the op-amp.
Most op-amps are connected with symmetrical voltage supplies, that is the voltages +Vs and −Vs are equal in magnitude. Example: ±9 V, ±15 V.
However, non-symmetrical supplies are also used. Example: +Vs = +20 V, −Vs = 0.
The op-amp circuit shown above is in the open-loop mode because the two inputs are not connected via circuit components or network to the output.
24.1.4 Characteristics of an Ideal Op-amp
An ideal op-amp in the open-loop mode has the following characteristics:
- (a) The voltage gain is infinite. Any voltage applied to the inputs would produce saturation voltage at the output.
- (b) Infinite input impedance.
- (c) Zero output impedance.
- (d) Infinite bandwidth.
24.1.5 Characteristics of a Practical Op-amp
A real op-amp in the open-loop mode has the following characteristics:
- (a) The voltage gain is very high, ranging between 103 – 106 at low frequencies. At high frequencies, the gain is very much lower.
- (b) The input impedance is high, ranging between 0.3 MΩ – 2 MΩ.
- (c) The output impedance is low, like 75 Ω.
- (d) The bandwidth is narrow. It could be as low as 10 Hz.
24.1.6 Op-amp as a Differential Amplifier
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| Figure 24.5 The figure shows an op-amp amplifying the voltage difference between the non-inverting (+) and inverting (−) inputs. |
1. The op-amp is a differential amplifier. It amplifies the difference Vd between the electric potential V1 at the + input and the electric potential V2 at the − input, as shown in Figure 24.5.
2. The amplified voltage appears as the output voltage Vo, which is measured relative to earth. In the open-loop mode, as shown, the value of Vo is very much greater than Vd.
24.1.7 Open-loop Voltage Gain
Suppose an op-amp is connected in the open-loop mode and suitable voltage supplies are connected to it.
Let
V1 = voltage applied at + input relative to earth
V2 = voltage applied at − input relative to earth
(Remember: + input for non-inverting; − input for inverting)
Then the potential difference Vd across the inputs is
Vd = V1 − V2
This potential difference is amplified by the op-amp. Let the amplified value be AOL. Then the output voltage Vo will be
Vo = AOL Vd
About AOL:
- (a) It is known as the open-loop voltage gain of the amplifier.
- (b) Its value is very high, ranging between 105 – 108.
- (c) Often it is given the unit of decibel (dB).
24.1.8 Sign of the Output Voltage
We have
Vo = AOL Vd
Vd = V1 − V2
The sign of Vo is determined by the sign of Vd. We have the following:
(a) If V1 at + input is more positive than V2 at − input, then Vd and Vo are positive.
We have non-inverting prevailing over inverting, causing Vo to be positive.
(b) If V1 is less positive than V2, then Vd and Vo are negative.
We have inverting prevailing over non-inverting, causing Vo to be negative.
EXAMPLE 24.1
V1 V2
(a) +100 μV +95 μV
(b) +100 μV +160 μV
(c) +20 μV −29 μV
(d) −20 μV +25 μV
(e) −150 μV −200 μV
V1 V2
(f) −150 μV −120 μV
(g) +10 μV 0 V
(h) −10 μV 0 V
(i) 0 V +20 μV
(j) 0 V −25 μV
Answer
(a) V1 = +100 μV (+ input) is more positive than V2 = +95 μV (− input). We have non-inverting prevailing over inverting. Hence, Vd and Vo are positive.
Vd = V1 − V2
= (+100) − (+95) = +5 μV
Vo = AOL Vd
= (105)(5 × 10−6) = +0.5 V
(b) V1 = +100 μV, V2 = +160 μV. We have inverting prevailing over non-inverting. Hence Vo is negative.
Vd = (+100) − (+160) = −60 μV
Vo = (105)(−60 × 10−6) = −6.0 V
(c) V1 = +20 μV, V2 = −29 μV. We have non-inverting prevailing over inverting. Hence Vo is positive.
Vd = (+20) − (−29) = +49 μV
Vo = (105)(49 × 10−6) = +4.9 V
(d) Vd = (−20) − (+25) = −45 μV
Vo = (105)(−45 × 10−6) = −4.5 V
(e) Vd = (−150) − (−200) = +50 μV
Vo = (105)(50 × 10−6) = +5.0 V
(f) Vd = (−150) − (−120) = −30 μV
Vo = (105)(−30 × 10−6) = −3.0 V
(g) Vd = (+10) − 0 = +10 μV
Vo = (105)(10 × 10−6) = +1.0 V
(h) Vd = (−10) − 0 = −10 μV
Vo = (105)(−10 × 10−6) = −1.0 V
(i) Vd = (0) − (+20) = −20 μV
Vo = (105)(−20 × 10−6) = −2.0 V
(j) Vd = (0) − (−25) = +25 μV
Vo = (105)(+25 × 10−6) = +2.5 V
24.1.9 Saturation of Output Voltage
1 Meaning of saturation voltage
We have Vo = AOL Vd
If the value of Vd increases continuously, the value of Vo will also increase continuously. However, the value of Vo does not continue to increase without limit. When Vo reaches certain value, it will not increase any more, even though Vd continues to increase. This maximum voltage of Vo is the saturation voltage.
2 Values of saturation voltage
One quantity which determines the value of the saturation voltage is the supply voltage Vs which is applied to the amplifier. The saturation voltage is about 0.9Vs, i.e.,
Vsat = 0.9Vs
Example: Let Vs = ±15 V. Then Vsat = ±14 V.
3 Order of magnitude of Vd to produce Vsat in open-loop mode
Let
Vd = Vsat / AOL
AOL ranges between 105 – 108. Hence, we have Vd between
Vd ≈ 10 V / 108 = 0.1 μV
and
Vd ≈ 10 V / 105 = 0.1 mV
Hence, if the op-amp is in the open-loop mode, the output voltage can very easily become saturated if the difference of the potentials of the two inputs, Vd, is less than a fraction of a millivolt.
EXAMPLE 24.2
Supply voltages of ±15 V are connected to an op-amp which has an open-loop gain of 105. Estimate the maximum value of Vd which could cause the output voltage of the amplifier connected in the open-loop mode to saturate.
Answer
Vsat = ±0.9Vs
= ±0.9(15)
= ±14 V
Vsat = AOL Vd
Vd = Vsat / AOL
= 14 V / 105
= 0.14 mV
24.1.10 Graph of Vo against Vd for Op-amp in Open-loop Mode
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| Figure 24.6 The figure shows the graph of output voltage against differential input voltage, where the linear region is limited by saturation levels beyond which the output remains constant. |
For an op-amp used in the open-loop mode, we have
Vo = AOL Vd
This means that
Vd ∝ Vo
This linear relationship is true only up to the saturation voltage, Vsat. The output voltage Vo will be constant for any further increase of Vd if saturation has taken place. This fact is shown in the graph of Vo against Vd in Figure 24.6. Notice the following:
(a) If the scale of the Vd-axis is in μV, we will get a slanting line PQ which passes through the origin and runs linearly up to the saturation voltage, after which we will get horizontal lines QR and NP.
(b) If the scale of the Vd-axis is in mV, then the slanting line PQ will not be visible. We will now get two horizontal lines passing through the saturation voltage.
EXAMPLE 24.3
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| Figure 24.7 The figure shows an op-amp with a sinusoidal differential input voltage applied across its inputs in open-loop mode. |
A differential voltage of Vd = (2 V sin(100πt)), where t is time, exists across the two inputs of an op-amp used in the open-loop mode, as shown in Figure 24.7.
The amplifier has a voltage gain of 100 000. For each of the circuits shown, sketch a graph of output voltage Vo against time t.
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| Figure 24.8 The figure shows the output voltage waveform of an op-amp with very high gain, where the signal quickly reaches saturation, resulting in a clipped waveform. |
24.1.11 Magnitude of Input Currents and Vd
1 Magnitude of the two input currents
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| Figure 24.9 The figure shows an op-amp with extremely small input currents at both inputs, which are assumed to be zero due to very high input impedance. |
The impedance of each input is very high. Because of this, currents i1 and i2 which flow into or out of the inputs are extremely small, as shown in Figure 24.9. They may be assumed to be zero. Hence, for an ideal op-amp we are going to make the following assumption:
i1 = 0
i2 = 0
2 Magnitude of Vd
We have Vd = V1 − V2
Because the two input currents are very small, the differential voltage Vd across the two inputs is also very small. For an ideal op-amp we make another assumption:
Vd = 0
24.1.12 Instability of AOL
The open-loop gain, AOL, of an op-amp used in the open-loop mode is a value which is not easy to keep constant. Consider the following facts:
- (a) Suppose an op-amp found in a circuit with an open-loop gain of 100 000 is damaged. We can replace the damaged op-amp with another similar one. However, the circuit with the newly replaced op-amp connected may not get back a gain of exactly 100 000. The gain is dependent on the parameters of the op-amp.
- (b) Increase in temperature of the circuit components and the op-amp itself can change the value of AOL.
- (c) In the open-loop mode, the amplifier has a very narrow bandwidth. If the amplifier operates beyond this narrow bandwidth, the gain drops very fast.
1. Inverting Amplifier
An inverting amplifier produces an output that is opposite in phase to the input signal.
It is widely used in signal processing where phase inversion is required.
2. Non-Inverting Amplifier
This amplifier produces an output signal that is in phase with the input signal.
It provides high input impedance and is commonly used in buffering applications.
3. Voltage Comparator
The op-amp compares two input voltages and outputs a high or low signal depending on which is greater.
4. Integrator
An integrator circuit produces an output proportional to the integral of the input signal.
5. Oscillator
Op-amps can be used to generate continuous waveforms without external input signals.
By understanding key concepts such as open-loop gain, saturation, and input characteristics, you can analyze and design various electronic circuits effectively.
Both ideal and practical op-amp models provide valuable insight into real-world applications, making them fundamental in engineering, instrumentation, and signal processing systems.
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