Exercise 7.2 Input impedances

Given is the opamp circuit below. For the opamp, $r_{\mathit{in}}=1M\mathrm{\Omega }$, $r_{\mathit{out}}=75\mathrm{\Omega }$, DC voltage gain $A_{\mathit{DC}}=10^5$, open-loop unity-gain bandwidth $f_{\mathit{UG}}=$ 1 MHz, first order low-pass behavior. In the circuit, $R_1=10k\mathrm{\Omega }$.

a)

Formulate an expression for the (open loop) gain of the opamp.

Indicate if the following statements are true or false. Motivate your answers with a proper explanation or calculation.

b)

The absolute value of the input impedance of the circuit, $|z_{\mathit{in}}|$, is higher than or equal to $R_1$ for all frequencies.

c)

The absolute value of the input impedance of the circuit, $|z_{\mathit{in}}|$, is higher than $R_1$ for at least one frequency.

d)

If you connect a capacitor in parallel to the port where $z_{\mathit{in}}$ is defined in the figure, the phase margin can get very small.

e)

If you connect a capacitor in parallel to the port where $z_{\mathit{in}}$ is defined in the figure, the gain margin can get very small.

f)

$|z_{\mathit{in}}|$ is higher at lower frequencies than at higher frequencies.

g)

If you connect an inductor in parallel to the $Z_{\mathit{in}}$ terminals, you may run into stability problems.