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I have the following SPICE parameters for an NPN 

IS=8.11E-14 BF=205 VAF=113 IKF=0.5 ISE=1.06E-11 
 + NE=2 BR=4 VAR=24 IKR=0.225 RB=1.37 RE=0.343 RC=0.137 CJE=2.95E-11 
 + TF=3.97E-10 CJC=1.52E-11 TR=8.5E-8 XTB=1.5

I am stuck on how to find Cpi ( from hybrid pi model) from the SPICE parameters.

Is the below assumption correct?

Cu = CJC
Cpi = 2*CJE + gm * TF

where gm is IC/VT under standard conditions

Melvin
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  • I highly recommend you draw a schematic, way easier to read than a list of values. – Juan Nov 05 '19 at 04:33
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    @Juan this is the format of standard SPICE parameters. There is no schematic. – Melvin Nov 05 '19 at 04:46
  • @Mel It's been a while and I'll need to verify my memory, but my recollection is that CJE and CJC are two of the five added to the ***non-linear*** hybrid-\$\pi\$ \$EM_2\$ model, which is a modification to the [earlier DC-only \$EM_1\$ model](https://electronics.stackexchange.com/a/252199/38098). (Lacking basewidth modulation and \$\beta\$ variations over collector current, not added until \$EM_3\$.) The early \$EM_1\$ model included three equivalent models called the transport, injection, and hybrid-\$\pi\$ and ***all of them*** were large-scale non-linear models. – jonk Nov 05 '19 at 05:24
  • @Mel The ***linearized*** hybrid-\$\pi\$ model derives from finding the derivative around an operating point of the \$EM_1\$ non-linear hybrid-\$\pi\$. By the time \$EM_2\$ came about, the transport and injection versions had been largely cast aside and the new AC (and DC) additions to \$EM_2\$ included CJE and CJC and three other capacitors, plus three resistors, and were only added to the earlier \$EM_1\$ hybrid-\$\pi\$ model. Of those five capacitors, only ***one*** of them is a constant (the substrate capacitor.) The other four, which include CJE and CJC are ***non-linear*** capacitors. – jonk Nov 05 '19 at 05:24
  • @Mel Therefore, when discussing the linearized (derivative/slope at an operating point) hybrid-\$\pi\$ with \$C_\pi\$, you are talking about a linearized version of the non-linear hybrid-\$\pi\$ \$EM_2\$ model. As CJE and CJC are non-linear capacitances that have to be linearized around an operating point, it's not really possible to convert them directly to \$C_\pi\$ through some simple formula. (Not as I recall, anyway. Instead, you have to start with the non-linear version and develop the linearized-about-an-operating-point equivalent in order to find \$C_\pi\$.) Been 30+ years, though. – jonk Nov 05 '19 at 05:31
  • @Mel I believe these are two capacitances do depend on \$g_m\$ but also the emitter-base (or collector-base) barrier potential and the emitter-base capacitance gradient. To characterize those 5 capacitances (four of them non-linear) and the three added resistances to \$EM_2\$, a total of twelve extra parameters were added to the \$EM_2\$ modeling. These include the forward and reverse transit times as well as two gradients and two barrier potentials. So I'm pretty sure there's more to it than you indicated in your formula. But I'm no expert on this. Just a hobbyist who reads a thing or two. – jonk Nov 05 '19 at 05:43

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In 'The Spice Book' from Vladimirescu it is

Cu = TR * gmR + CJC

Cpi = TF * gmF + CJE

JosefC
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