Electrical – finding open circuit voltage gain

feedbackgainnegative feedbacktransistors

below I have this schematic to find the open circuit voltage gain. This circuit basically utilizes three resistors from which R_f is supposed to be the internal feedback resistor. It also utilizes the voltage controlled current source. My job is to find A_vo = v_o/v_i. My work is illustrated below
\begin{equation}
A_{vo}\:=\:\frac{v_o}{v_i};\:v_o\:=\:-g_mv_iR_2\: therefore \:A_{vo}=-g_mR_2
\end{equation}
but the exact answer looks like this:
\begin{equation}
\:A_{vo}=-g_mR_2\:\frac{1-\frac{1}{g_mR_f}}{1+\frac{R_2}{R_f}}
\end{equation}
somehow am having trouble incorporating R_f into the equation. Any help please?

* My apologies, in the schematic, the dependant source is a voltage controlled current source*

circuit schematic

Best Answer

Part of the current of the transconductance amplifier will flow back to the input rather than through \$R_2\$. So the KCL law in the output is not

$$g_mv_i + \frac{v_o}{R_2} = 0$$

As this will lead to your incorrect expression. But the correct KCL law would be:

$$g_mv_i + \frac{v_o}{R_2} + \frac{v_o-v_i}{R_f} = 0$$

Solving this will result in the exact expression given.