How do I find the input impedance of this common emitter amplifier?

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\$V_{CC}\$ is supposed to be at the top of \$R_5\$. I forgot how to do the analysis to find the input impedance. The input goes in through the blocking capacitor, \$C_8\$, the output comes out from the collector of the NPN.


3 Answers 3


\$V_{CC}\$ is small signal ground so \$R_3\$ is connected to small signal ground along with \$R_4\$ (and therefore they are in parallel with one another). This resistance is in parallel with the impedance looking into the base of the transistor, which is \$r_{\pi} + (\beta + 1)Z_E\$, where \$Z_E = R_6 \parallel C_{19}\$. This total impedance is in series with \$C_8\$. Summarizing:

$$Z_{\text{in}} = \frac{1}{sC_8} + R_3 \parallel R_4 \parallel \left(r_{\pi} + (\beta + 1)\frac{R_6}{sR_6C_{19}+1}\right)$$

Generally, at frequencies of interest the capacitors can be regarded as short circuits, in which case \$Z_E = 0\$ and the input impedance simplifies to

$$Z_{\text{in}} = R_3 \parallel R_4 \parallel r_{\pi}$$

  • \$\begingroup\$ I looked through two datasheets for the 2N3904 and couldn't find values for r_pi or for Beta. Do I calculate these or are they determined by some other method? \$\endgroup\$
    – Jucesanc
    Mar 10, 2015 at 20:06
  • 1
    \$\begingroup\$ You generally have to assume \$\beta = h_{\text{FE}}\$. And \$r_{\pi}\$ is determined by \$I_C\$. See here. \$\endgroup\$
    – Null
    Mar 10, 2015 at 20:12

The simplest solution applies to frequecies only above the cut-off frequencies of the high-pass effects which are caused by C8 as well as C19. In this case, it is simply Zin=R3||R4||rbe. The dynamic resistance rbe is identical to the small-signal parameter hie (or h11) and we have rbe=hfe/gm=beta/gm (beta: current gain; gm: transconductance at the selected bias point).


To test what the input impedance actually is, 1) Put a variable resistor in series with the input to the amplifier, 2) Send in a signal with known peak to peak voltage, 3) Measure the voltage across the variable resistor, 4) Turn the resistor so that the peak to peak voltage is exactly half the peak to peak voltage of the input signal. 5) Measure the variable resistor

That's your input resistance, try different frequencies to get a plot of frequency Vs input impedance.


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