Anyone measure BJT internal capacitances like this ? - Page 1
Forum section: electronics / projects

author: MathWizard
author_rank: Super Contributor
timestamp: July 22, 2023, 08:36:12 pm
content: Here's a lab pdf on a test circuit for finding Cbe and Cjc of a BJT, and it must take quite a while to do all the steps and calculations and/or programming for plots. But I would like to try IRL. Some of the wording could be better.https://my.ece.msstate.edu/faculty/winton/CDNuE/Labx/lab11x.pdfBasically they do 2x4 tests, some with a max non-logarithmic gain of -1, others -2. And some tests use 2 BJT's in parallel. There are 5 input resistance steps, and you sweep the Vin and find the -3dB frequency of Vc/Vb.Then you have to repeat the whole thing with 2 JFET's , I think to cancel out 2 extra wiring capacitance's.From those 4x4 steps you get 4 sets of C1 to C4 , that you can then solve for Cbe and Cjc, / Cpi and Cu.They do it on a breadboard. I made a version in LTspice but I haven't gone through all the steps and gotten the C values.If you made the test jig on a protoboard, the type with just the little ring pads, or on a copper clad board, can you make that in such a way to ignore the extra wiring capacitance's and skip some steps ?IDK all the equations for the semiconductor level stuff yet either, but I've seen a few like relating to forward base transit time. Can someone point me at a pdf or equations, that would let me calculate with an equation or 2, Cpi and Cu from the main LTspice values related to capacitance?So I mean if I calculate my DC operating points, and have the basic AC model, with just r_pi and and r_o, and a current source, what's the easiest way to use some LTSpice parameters like CJC and CJE to get reasonable values of Cpi and Cu. Assuming they aren't the same, and it's not that simple.

author: moffy
author_rank: Super Contributor
timestamp: July 23, 2023, 12:34:57 am
content: See:https://electronics.stackexchange.com/questions/465835/how-to-find-cpi-in-hybrid-pi-model-of-transistor-from-spice-parametersfor a brief discussion of the hybrid pi capacitances. It appears that they are non linear and not just in the voltage dependent sense.

author: MathWizard
author_rank: Super Contributor
timestamp: July 23, 2023, 04:26:04 pm
content: Ok I was getting close, I found some more eqns, I use Cpi=Cje+ge*tau_F since I don't ignore the base current.But for the BC junction/depletion region capacitance. Besides a datasheet or a sim, I can't find the unity gain Freq f_T, so I can't use that to get Cjc. from the sum of Cpi and Cu. I see some deeper level eqns for just PN junction capacitance, but they need doping concentrations and so on.I know TR from spice param's, but what are they calling the gmR, is that reverse gm of the reverse diode in the more detailed Ebers-Moll model ? That seems like back to doping levels and current densities.In the below pic, the 2Cu in eq 2 looks wrong (from the log equations, I think the 2 was supposed to be a squared, f_T=sqrt(B^2-1)/(2pi*rpi*(Cpi+Cu)) ), but a few pdf's have these basic equations, but none have said yet how to get Cu or f_T without knowing Cu+Cpi or something else I'm missing, like the C_M capacitance I've seen before, and something to the power of M.A lot of little notation differences across the pdf's I'm looking at too, that doesn't help.

author: moffy
author_rank: Super Contributor
timestamp: July 23, 2023, 07:17:07 pm
content: Did a quick check, it looks like gmr = 1/ro where ro is the output impedance which makes sense.

author: MathWizard
author_rank: Super Contributor
timestamp: July 25, 2023, 01:28:00 pm
content: So using Cu=Cj0+TR/ro, leads to larger Cu as the Ic increasesI found this equation, like the diode version I saw but without any mention of the junction area. However, assuming they mean the DC value of Vcb, then for any typical Vcb value in the active region, you get a negative under the the radical, I don't think they want that. Is that equation wrong, or what do they mean ? Changing the sign or using addition, I get ~4pF, which is less than Cj0=8pF, and Cu gets smaller for higher Vcb.Or is Cj0=8pF, is that at 10V at 1MHz like in a datasheet, ?? But in LTspice, CJC=8pF, and they call that the zero voltage built in potential.I made a 2N2222 circuit and it's gain was down 10% from expected at only 2MHz, and using the Cpi, and Cu of anything near 8pF, gets pretty close, at 2MHz anyways.I can follow along with most of the semiconductor level derivation, I guess I better write some of it down.If these effects start at such low frequency, what Cu and Cpi eqns do people use ? Don't people working on radio's use these equations all the time ?

author: moffy
author_rank: Super Contributor
timestamp: July 25, 2023, 02:06:56 pm
content: I would go with what you know and understand, I think there are a lot of approximations going on to try and make such complex formulas manageable, SPICE is at best a reasonable approximation but even then models go through various revisions and sometimes complete revamps. For radio, at least the higher frequencies 'S' parameters appear popular.

author: MathWizard
author_rank: Super Contributor
timestamp: July 27, 2023, 12:08:23 pm
content: Ok it is supposed to be a positive sign in that equation for Cu. I tried a BC547B using a bunch of of the spice parameters, like the MJC grading factor, and it matches the output magnitude very well, but not the phase tho, it's quite a bit off. But that's the closest I've ever modelled a BJT to the sim or real life.And then I see why they use Miller's theorem in a feedback amplifier. I've heard about that before, but never tried till now.Sometime soon I'm going to try that test circuit. Looking up internal capacitance test circuits, I haven't found much else so far.

author: MathWizard
author_rank: Super Contributor
timestamp: July 29, 2023, 11:48:08 pm
content: On a piece of proto-board, made this common-base BJT amp to use in a Colpitts oscillator. And the DC values match pretty well to what I calculate from LTSpice parameter's for this BC547B.And making an AC model circuit from the spice param's matches well enough for now, to the sim of the BJT.In real life, the 1kHz gain is 42.4dB~133V/V, a bit higher than the sim with 124V/V. But IRL the -3dB point is only ~444kHz, vs in the sim, it's more like 27MHz.I have my AWG on 50 Ohm output impedance, and with a 10x probe on the emitter, and the scope is not on 50R. And I'm upping the Vin until I see 10mVrms on the emitter.Then I upped the frequency to about the -3dB point, and after a little fine adjustment I have about 10mVrms on the emitter again, and 39.4dB ~94V/V on the collector.So what's causing that roll-off that's not in the sim ? Is it mainly the 2 scope probes ? I see adding 15pF to the emitter and 25pF to the collector gets a roll off closer to 1.9MHz in the sim.Ok I see having both on probes on 10x, pushes the -3dB point out to around 3MHz. I only calulated 1.7pF as Cu, so yeah I'm not used to noticing how massive the probe capacitance is, or how much it would affect a BJT. So really I'd need to attach a coax cable connectors to my circuit, and get the accessories for all that.