# Simulation not converging with theory - BJT's

Discussion in 'Homework Help' started by bennyq, Mar 2, 2015.

1. ### bennyq Thread Starter New Member

Sep 13, 2014
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0

I am simulating the above circuit, by theory Ic = Hf * Ib. When i simulate a circuit such as this in LTspice, this formula isn't holding up.. For instance in my LTspice, im using a 2N3904 NPN, Vcc=6V Rb=300K and Rc=1k..
Ib=17.67uA and Ic=5.23mA(in sim). The model has a Bf=300, so Ib*300 = 5.3mA, albeit close, but still some error that id like to account for?

My 2N3904 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=Philips).

2. ### WBahn Moderator

Mar 31, 2012
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4,917
The phrase "simulation is not converging" has a very specific meaning -- namely that the simulation could not find a solution and crashed.

The error isn't in the simulator, it's in your hand calculation. The collector current in a real transistor is not as simple as just Hf*Ib. It is dependent on several things, some of which are nonlinear. The Hf itself is dependent on many parameters in a nonlinear way. One of the big things, at a given temperature, is the Early effect, which describes the fact that the collector current increases if the collector-emitter voltage is increased (and the base current is held constant). The transistor models these more subtle effects in order to give you more accurate simulation results than you could possibly (or at least reasonably) do by hand.

The transistor model used by LTSpice is almost certainly the Gummel-Poon model, which has over 40 parameters to characterize the behavior of the transistor. For modern IC design this isn't anywhere near close enough to the actual behavior. I've worked with processes in which each transistor was modeled as a subcircuit involving as many as 300 components, some of which were transistors that used BSIM Level 7 models that go way beyond the Gummel-Poon.

3. ### JoeJester AAC Fanatic!

Apr 26, 2005
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• ###### 2N3904-various-models.txt
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Last edited: Mar 2, 2015