Description
Problem 1: DC analysis of inverting and non-inverting amplifiers
R1
R2
Vout
Vin
R1
R2
Vout
Vin
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) (5 points) 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) (2.5 points) 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) (2.5 points) 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
vout
C
R
iin
iin
t
0
imax
ton
t = 0
Figure 2a. Current-input integrator Figure 2b. Input current pulse
For the following, assume ideal opamp behavior.
a) (2.5 points) Determine an expression for the transfer function vout/iin.
b) (5 points) 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 (2 points): 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
R3
R4
vout
vim
vip
R2
R1
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) (2.5 points) Sketch the Bode magnitude and use the graph to approximate the 3dB bandwidth.
Sketch the Bode phase plot.
b) (5 points) 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) (5 points) What is the resistance “looking into” each input (vim and vip)?
d) (5 points) Check your answers to Parts b and c in Ltspice using the Analog Devices opamp model
for the AD8691.
