[SOLVED] UWEE538 Homework 4

Description

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 R_in, and output resistance R_out. 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.

1. (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 (V_out/V_in).
   2. Closed-loop output resistance.
   3. Closed-loop input resistance.
2. (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.
3. (2.5 points) Assuming the opamp has a voltage offset v_OS, what is the resulting output offset for each structure? Assume A₀ → . Check your answer in Ltspice.
4. (2.5 points) Assuming the opamp has input bias current I_B, 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.

2. (2.5 points) Determine an expression for the transfer function v_out/i_in.
3. (5 points) Determine an expression for the transient response of the circuit. What is the value of v_out (in terms of R, C, i_max, and t_on) at time t = t_on?

Bonus (2 points): Design the circuit (i.e. determine R and C) to function as an integrator, such that             v_out(t_on) = i_max/C with less than 0.1% error. Use i_max = 10µA and ensure v_out 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 (f_T) of 10MHz but is otherwise ideal (R_in =  and R_out = 0). R₁ = R₂ = R₃ = R₄ = 10k.

2. (2.5 points) Sketch the Bode magnitude and use the graph to approximate the 3dB bandwidth. Sketch the Bode phase plot.
3. (5 points) Calculate the DC gain and 3dB bandwidth of the closed-loop transfer function v_out/(v_ip – v_im). Sketch the Bode magnitude and phase of the closed-loop transfer function.
4. (5 points) What is the resistance “looking into” each input (v_im and v_ip)?
5. (5 points) Check your answers to Parts b and c in Ltspice using the Analog Devices opamp model for the AD8691.