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UWEE538-Homework 4 DC Analysis of Inverting and Non-inverting Amplifiers Solved
Problem 1: DC analysis of inverting and non-inverting amplifiers
R2 R2
Figure 1a. Inverting amplifier Figure 1b. Non-inverting amplifier
For the two amplifiers shown above, the opamp has open-loop DC gain A0, input resistance Rin, and output resistance Rout. For the Ltspice parts, use the UniversalOpamp2 (SpiceModel level.1), with R1 = 1k and R2 = 10k. The default open-loop output resistance for the opamp model is 0.1. You can use the ‘DC Transfer’ analysis.
a) For the inverting and non-inverting amplifiers shown in Fig 1a and 1b, determine expressions for each of the following assuming A0 → (infinite open-loop gain). Provide comments on how each closed-loop parameter compares to its open-loop counterpart.
1. Closed-loop gain (Vout/Vin).
2. Closed-loop output resistance.
3. Closed-loop input resistance.
b) (5 points) Repeat Part a assuming A0 is finite. Try to develop some intuition regarding how each parameter depends on A0 and the feedback factor . Check your answer by setting A0 → and comparing to your answer in Part a.
c) Assuming the opamp has a voltage offset vOS, what is the resulting output offset for each structure? Assume A0 → . Check your answer in Ltspice.
d) Assuming the opamp has input bias current IB, what is the resulting output offset for each structure? Assume A0 → .
Problem 2: Opamp circuit transient response
Figure 2a. Current-input integrator Figure 2b. Input current pulse
For the following, assume ideal opamp behavior.
a) Determine an expression for the transfer function vout/iin.
b) Determine an expression for the transient response of the circuit. What is the value of vout (in terms of R, C, imax, and ton) at time t = ton?
Bonus : Design the circuit (i.e. determine R and C) to function as an integrator, such that vout(ton) = imax/C with less than 0.1% error. Use imax = 10µA and ensure vout doesn’t exceed a bipolar supply voltage of 2.5V. Verify your design in Ltspice.
Problem 3. Difference amplifier
Figure 3. Difference amplifier
For the following, the opamp has a DC gain (A0) of 100 dB and a unity-gain bandwidth (fT) of 10MHz but is otherwise ideal (Rin = and Rout = 0). R1 = R2 = R3 = R4 = 10k.
a) Sketch the Bode magnitude and use the graph to approximate the 3dB bandwidth. Sketch the Bode phase plot.
b) Calculate the DC gain and 3dB bandwidth of the closed-loop transfer function vout/(vip – vim). Sketch the Bode magnitude and phase of the closed-loop transfer function.
c) What is the resistance “looking into” each input (vim and vip)?
d) Check your answers to Parts b and c in Ltspice using the Analog Devices opamp model for the AD8691.
R2 R2
Figure 1a. Inverting amplifier Figure 1b. Non-inverting amplifier
For the two amplifiers shown above, the opamp has open-loop DC gain A0, input resistance Rin, and output resistance Rout. For the Ltspice parts, use the UniversalOpamp2 (SpiceModel level.1), with R1 = 1k and R2 = 10k. The default open-loop output resistance for the opamp model is 0.1. You can use the ‘DC Transfer’ analysis.
a) For the inverting and non-inverting amplifiers shown in Fig 1a and 1b, determine expressions for each of the following assuming A0 → (infinite open-loop gain). Provide comments on how each closed-loop parameter compares to its open-loop counterpart.
1. Closed-loop gain (Vout/Vin).
2. Closed-loop output resistance.
3. Closed-loop input resistance.
b) (5 points) Repeat Part a assuming A0 is finite. Try to develop some intuition regarding how each parameter depends on A0 and the feedback factor . Check your answer by setting A0 → and comparing to your answer in Part a.
c) Assuming the opamp has a voltage offset vOS, what is the resulting output offset for each structure? Assume A0 → . Check your answer in Ltspice.
d) Assuming the opamp has input bias current IB, what is the resulting output offset for each structure? Assume A0 → .
Problem 2: Opamp circuit transient response
Figure 2a. Current-input integrator Figure 2b. Input current pulse
For the following, assume ideal opamp behavior.
a) Determine an expression for the transfer function vout/iin.
b) Determine an expression for the transient response of the circuit. What is the value of vout (in terms of R, C, imax, and ton) at time t = ton?
Bonus : Design the circuit (i.e. determine R and C) to function as an integrator, such that vout(ton) = imax/C with less than 0.1% error. Use imax = 10µA and ensure vout doesn’t exceed a bipolar supply voltage of 2.5V. Verify your design in Ltspice.
Problem 3. Difference amplifier
Figure 3. Difference amplifier
For the following, the opamp has a DC gain (A0) of 100 dB and a unity-gain bandwidth (fT) of 10MHz but is otherwise ideal (Rin = and Rout = 0). R1 = R2 = R3 = R4 = 10k.
a) Sketch the Bode magnitude and use the graph to approximate the 3dB bandwidth. Sketch the Bode phase plot.
b) Calculate the DC gain and 3dB bandwidth of the closed-loop transfer function vout/(vip – vim). Sketch the Bode magnitude and phase of the closed-loop transfer function.
c) What is the resistance “looking into” each input (vim and vip)?
d) Check your answers to Parts b and c in Ltspice using the Analog Devices opamp model for the AD8691.
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