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Op Amp Equivalents

The questions below are due on Wednesday February 26, 2020; 11:59:00 PM.
 
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This problem studies the op-amp circuit shown below. Note that its output voltage is the voltage v_{OUT}. Assume that the op-amp is ideal. Also, assume that the circuit is stable. That is, assume that all voltages are finite for a finite input voltage v_{IN}.

Determine the Thevenin-equivalent voltage of the op-amp circuit at its output port as a function of the circuit parameters. Note that the output port is the port at which v_{OUT} is defined.

Use vIN for v_{IN}.

V_{Th}=

Determine the Thevenin-equivalent resistance of the op-amp circuit at its output port as a function of the circuit parameters. Note that the output port is the port at which v_{OUT} is defined.

R_{Th}=

Determine the Norton-equivalent current of the op amp circuit at its output port as a function of the circuit parameters. Note that the output port is the port at which v_{OUT} is defined.

Note the voltage is v_{IN} in this problem. Enter it as vIN

I_{N}=

If R_1 = R_2 = R, answer the following questions:

What happens to the Thevenin Voltage when R_1-R_2 = 0?

What happens to the Thevenin Resistance when R_1-R_2 = 0?

What happens to the Norton Current when R_1-R_2 = 0?

What standard component does the circuit appear as?

With R_1 = R_2 = R, the op-amp circuit is connected to a load resistor at its output port as shown below. Determine the current i_L into the load as a function of v_{IN}, R, and R_L.

Use vIN for v_{IN}.

i_L=

Assume that the op-amp output voltage v_{AMP} must satisfy |v_{AMP}| < V_S for the op-amp to operate properly. Still assuming that the op-amp circuit is connected to a load resistor as shown in the part above, and still assuming that R_1 = R_2 = R, determine the allowable range of R_L that ensures proper operation of the circuit. Do so in terms of v_{IN}, R and V_S. Also you may need to use abs() to express absolute value here (kinda sorta hint)

Note one voltage is v_{IN} in this problem. Enter it as vIN. Another is V_S. Enter it as VS.

Lower Bound on R_L:
Upper Bound on R_L: