## Description

For the two amplifiers shown above, the opamp has open-loop DC gain *A _{0}*, input resistance

*R*, and output resistance

_{in}*R*. For the Ltspice parts, use the UniversalOpamp2 (SpiceModel level.1), with

_{out}*R*= 1k and

_{1}*R*= 10k. The default open-loop output resistance for the opamp model is 0.1. You can use the ‘DC Transfer’ analysis.

_{2}- For the inverting and non-inverting amplifiers shown in Fig 1a and 1b, determine
*expressions*for each of the following assuming*A*→ (infinite open-loop gain). Provide comments on how each closed-loop parameter compares to its open-loop counterpart._{0 }- Closed-loop gain (
*V*/_{out}*V*)._{in} - Closed-loop output resistance.
- Closed-loop input resistance.

- Closed-loop gain (
- Repeat Part a assuming
*A*is finite. Try to develop some intuition regarding how each parameter depends on_{0}*A*and the feedback factor . Check your answer by setting_{0}*A*→ and comparing to your answer in Part a._{0 } - Assuming the opamp has a voltage offset
*v*, what is the resulting output offset for each structure? Assume_{OS}*A*→ _{0 }*.*Check your answer in Ltspice. - Assuming the opamp has input bias current
*I*, what is the resulting output offset for each structure? Assume_{B}*A*→ _{0 }*.*

** **

# Problem 2: Opamp circuit transient response

# Figure 2a. Current-input integrator Figure 2b. Input current pulse

For the following, assume ideal opamp behavior.

- ( Determine an expression for the transfer function
*v*/_{out}*i*_{in}. - Determine an expression for the transient response of the circuit. What is the value of
*v*(in terms of_{out}*R*,*C*,*i*, and_{max}*t*) at time_{on}*t*=*t*?_{on}

*Bonus ):* 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*= 10µA and ensure

_{max}*v*doesn’t exceed a bipolar supply voltage of 2.5V. Verify your design in Ltspice.

_{out}** **

# Problem 3. Difference amplifier

**Figure 3. Difference amplifier **

For the following, the opamp has a DC gain (*A _{0}*) of 100 dB and a unity-gain bandwidth (

*f*) of 10MHz but is otherwise ideal (

_{T}*R*= and

_{in}*R*= 0).

_{out}*R*=

_{1}*R*=

_{2}*R*=

_{3}*R*= 10k.

_{4}- Sketch the Bode magnitude and use the graph to approximate the 3dB bandwidth. Sketch the Bode phase plot.
- Calculate the DC gain and 3dB bandwidth of the closed-loop transfer function
*v*/(_{out}*v*–_{ip}*v*). Sketch the Bode magnitude and phase of the closed-loop transfer function._{im} - What is the resistance “looking into” each input (
*v*and_{im}*v*)?_{ip} - Check your answers to Parts b and c in Ltspice using the Analog Devices opamp model for the AD8691.