Objective: Design an inverting amplifier with a specified voltage gain. Specifications: The circuit configuration to be designed is shown in Figure 9.10. Design the circuit such that the voltage gain is Av = −5. Assume the op-amp is driven by an ideal sinusoidal source, vs = 0.1 sin ωt (V), that

Question

Objective: Design an inverting amplifier with a specified voltage gain. Specifications: The circuit configuration to be designed is shown in Figure 9.10. Design the circuit such that the voltage gain is [latex]A_{v} = −5[/latex]. Assume the op-amp is driven by an ideal sinusoidal source, [latex]v_{s} = 0.1 \sin ωt (V)[/latex], that can supply a maximum current of 5 μA. Assume that frequency ω is low so that any frequency effects can be neglected.
Design Pointer: If the sinusoidal input signal source has a nonzero output resistance, the op-amp must be redesigned to provide the specified voltage gain.

Accepted Answer

The input current is given by
[latex]i_{1} = \frac{v_{I}}{R_{1}} = \frac{v_{s}}{R_{1}}[/latex]

If [latex]i_{1}(max) = 5 μA[/latex], then we can write
[latex]R_{1} = \frac{v_{s} (max)}{i_{1}(max)} = \frac{0.1}{5 × 10^{−6}} ⇒ 20 k\Omega[/latex]
The closed-loop gain is given by
[latex]A_{v} = \frac{−R_{2}}{R_{1}} = −5 [/latex]

We then have
[latex]R_{2} = 5R_{1} = 5(20) = 100 k\Omega[/latex]
Trade-offs: If the signal source has a finite output resistance and the desired output voltage is [latex]v_{o} = −0.5 \sin ωt[/latex] , the circuit must be redesigned. Assume the output resistance of the source is [latex]R_{S} = 1 k\Omega[/latex].
Redesign Solution: The output resistance of the signal source is now part of the input resistance to the op-amp. We now write
[latex]R_{1} + R_{S} = \frac{v_{s} (max)}{i_{1}(max)} = \frac{0.1}{5 × 10^{−6}} ⇒ 20 k\Omega[/latex]
Since [latex]R_{S} = 1 k\Omega[/latex], we then have [latex]R_{1} = 19 k\Omega[/latex]. The feedback resistor is then [latex]R_{2} = 5(R_{1} + R_{S} ) = 5(19 + 1) = 100 k\Omega[/latex].
Comment: The output resistance of the signal source must be included in the design of the op-amp to provide a specified voltage gain.
Computer Verification: Figure 9.11(a) shows the PSpice circuit schematic with the source resistance of 1 kΩ and an input resistance of 19 kΩ. Figure 9.11(b) shows the 100 mV sinusoidal input signal. Figure 9.11(c) is the output signal which shows that a gain of 5 (magnitude) has been achieved and also shows that the output signal is 180 degrees out of phase with respect to the input signal. Finally, the input current is shown in Figure 9.11(d) with a maximum value of 5 μA. The actual circuit characteristics are not influenced to any great extent by the nonideal parameters of the μA-741 op-amp used in the circuit simulation

Question 9.1: Objective: Design an inverting amplifier with a specified vo...

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