Question $1$:

A multi$-$stage single$-$ended amplifier is shown in Fig. $1.$ Answer the following questions. Provide numerical answers when necessary.

Fig. $1$: A multi$-$stage single$-$ended amplifier assuming op$-$amps are ideal.

$($a$)$ Assuming ideal op$-$amp behavior, what is the DC gain of this circuit from input to output. Is the amplifier inverting or noninverting?

$[2$ points$]$

$($b$)$ Using the method of open$-$circuit time constants, identify the location of the poles of this circuit.

$[4$ points$]$

$($c$)$ What is the expected $3-$dB bandwidth of this circuit?

$[1$ points$]$

$($d$)$ Write a transfer function of the input$-$output behavior $\backslash (\backslash$left$(\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$o$\}\}/\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$i$\}\}\backslash$right$)\backslash )$ of this amplifier.

$[2$ points$]$

$($e$)$ If this amplifier is to be used in a closed$-$loop arrangement with $\backslash (\backslash$beta$=1\backslash ),$ is the open$-$loop circuit stable?

$[1$ points$]$