- #1
Corneo
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I would like to find the transconductance of such circuit. I am choosing to ignore r_0 for the time being and going with the definition
G_m = \frac {i_0}{v_i} \bigg |_{v_i = 0},
What I did first was notice that i_0= - g_m v_\pi[/itex] <br /> <br /> v_i appears as the top node voltage at r_\pi w.r.t to ground. Then I have a voltage divider and using the impedance reflection rule, I have the relationship v_\pi = \frac {r_\pi}{r_\pi + (\beta + 1)R_{EA}}v_i, then G_m = -\frac {g_m v_\pi r_\pi}{r_\pi + (\beta + 1) R_{EA} } = - \frac {g_m}{1+( \frac{\beta + 1}{r_\pi})R_{EA}}<br /> Then I use r_\pi = \frac {\beta}{g_m} and \beta &gt;&gt; 1, so G_m = -\frac {g_m}{1 + g_mR_{EA}}. Is this correct?
G_m = \frac {i_0}{v_i} \bigg |_{v_i = 0},
What I did first was notice that i_0= - g_m v_\pi[/itex] <br /> <br /> v_i appears as the top node voltage at r_\pi w.r.t to ground. Then I have a voltage divider and using the impedance reflection rule, I have the relationship v_\pi = \frac {r_\pi}{r_\pi + (\beta + 1)R_{EA}}v_i, then G_m = -\frac {g_m v_\pi r_\pi}{r_\pi + (\beta + 1) R_{EA} } = - \frac {g_m}{1+( \frac{\beta + 1}{r_\pi})R_{EA}}<br /> Then I use r_\pi = \frac {\beta}{g_m} and \beta &gt;&gt; 1, so G_m = -\frac {g_m}{1 + g_mR_{EA}}. Is this correct?
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