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I have a common base amplifier with a source resistance and a load resistor. I am trying to solve for the system gain including the source resistor with both the hybrid-pi and T model but seem to be getting different answers.

When solving the hybrid-pi model for Vbe by looking at the currents at the emitter I end up with an extra gm term due to the voltage controlled current source. I do not get this term when I solve for the same circuit with the T-model. Any help? Its probably something simple I am missing.

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  • \$\begingroup\$ You need to show your circuit and specify exactly what "gain" is in your context. Is it a voltage ratio? Current ratio? Power ratio? Ratio of what to what exactly. Without proper units and definitions this is just handwaving, not engineering. \$\endgroup\$
    – Olin Lathrop
    Commented Feb 25, 2013 at 13:35

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Without the equations you get it's hard to know exactly what's going on, but you wouldn't expect to get a "gm" term when you solve for the gain T model, as the model consists of a current controlled current source Beta*ib in series with the dynamic emitter resistance. The two are related, however, as Beta*ib = (Beta/r_pi)*v_pi = gm*v_pi. For the T model of a common base amplifier with source resistance Rs and load resistance RL, one should get the gain as being (alpha*RL)/(Rs + Re), with Re being the dynamic emitter resistance.

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  • \$\begingroup\$ That is the gain I get for the T model. For the hybrid-Pi model I get: Vo/Vi = (gmRlRpi) / (gm * Rs * Rpi + Rs + Rpi). The difference is that gm term on the bottom when the equation is simplified down. That extra term comes from when I solve for the currents coming into and out of the emitter. As the base is grounded Ve determines Vbe so I get: Ve/Rpi = gm(-Ve) + (Vs-Ve)/Rs The gm(-Ve) term propagates through and causes the gm * Rs * Rpi difference in the final answer. Thanks. \$\endgroup\$
    – Zhukov
    Commented Apr 28, 2011 at 0:55

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