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I would like to accurately simulate a basic CE amplifier that I have soldered and probed with a 10 MHz sine wave applied to the input.

My amplifier Zin simulations yield a negative resistive component when Q1 is bypassed by C2. Probing with oscilloscope at the collector of Q1, the bypassed circuit provides much greater voltage amplification.

I interpret this as: When my input signal voltage rises, current into the amplifier would decrease, and when the input signal voltage falls, current into the amplifier would increase. Rephrased, a negative resistance causes a 180 degree phase offset between voltage and current. Both are still making their way to the amplifier.

Would this mean that the amplifier would still amplify as one might expect, but with a different phase offset between input and output voltage than the usual 180 degrees of an inverting amplifier?

50 ohms Example 1 (Convention): Multiplying the expression for input impedance looking into R4 by (-1) yields the correct input impedance of 50 ohms instead of -50 ohms.

unbypassed Example 2 (Unbypassed) Without C2 connected, the resistive term of impedance looking into C1 at n004 is positive.

bypassed Bypassing R3 with C2 results in a negative resistive impedance component.

Transistor model:

.model 2N3904 NPN(
 IS=1E-14
 VAF=100
 Bf=300
 IKF=0.4
 XTB=1.5
 BR=4
 CJC=4E-12
 CJE=8E-12
 RB=20
 RC=0.1
 RE=0.1
 TR=250E-9
 TF=350E-12
 ITF=1
 VTF=2
 XTF=3
 Vceo=40
 Icrating=200m
 mfg=NXP
)

(line breaks added for legibility)

Update:

enter image description here Using an AC 1 current source and dividing input node voltage by "1A" to get ohms while setting y-axis to a linear bode blot yields a positive resistive impedance.

enter image description here Changing the y-axis mode to Cartesian instead of a bode plot results in a negative resistive impedance.

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  • \$\begingroup\$ I'm not getting the same results. I have several different models for the 2N3904 and they give different results but none show a negative resistance. Can you add the .model statement for the transistor you are using to your question? \$\endgroup\$ Commented Aug 8 at 23:21
  • \$\begingroup\$ @GodJihyo Sure; added. \$\endgroup\$ Commented Aug 8 at 23:23
  • \$\begingroup\$ been a while since I looked at SPICE models of transistors, but isn't IS the saturation current, and isn't 10 femtoampere a bit low? \$\endgroup\$ Commented Aug 8 at 23:43
  • \$\begingroup\$ Okay, that's the default LTspice model then. I have the same schematic and same model but I get around 5kΩ @ 1MHz dropping to around 20Ω @ 100 MHz. I don't know why our results should be different. \$\endgroup\$ Commented Aug 8 at 23:44
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    \$\begingroup\$ @GodJihyo yeah, it gets multiplied with exp(V_BE / (25 mV)) - 1 (at room temp), which very quickly gets very large. \$\endgroup\$ Commented Aug 8 at 23:48

1 Answer 1

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You are probably experiencing negative input impedance due to Miller effect, that is, the collector signal coupling in to the base via the collector-base capacitance.

This is the results I get when I plot the real part of the parallel input resistance and the parallel input capacitance. The magnitude of the input impedance remains positive. This is using the 2N3904 model supplied by LTspice which is the same as what you posted.

inputZ

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  • \$\begingroup\$ Interesting. Would the positive Zin magnitude suggest that the amplifier is not sourcing current to whatever is connected to its base regardless of the negative real input resistance? \$\endgroup\$ Commented Aug 9 at 5:22
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    \$\begingroup\$ @YousifAlniemi You need to combine phase with magnitude to make any sense of what the input impedance is. This is why I always use complex impedance when analyzing circuit impedance. \$\endgroup\$ Commented Aug 9 at 17:26
  • \$\begingroup\$ @YousifAlniemi You may want to try a cascode topology which gets rid of the Miller effect. \$\endgroup\$ Commented Aug 10 at 4:28
  • \$\begingroup\$ with negative input impedance it means that the amplifier is delivering power back to the source? @qrk \$\endgroup\$ Commented Aug 10 at 16:09

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