**EMRFD Message Archive 814**

MessageDateFromSubject814 2007-05-30 19:50:12 kanewderfish AC formulas on p2.25 vs FBA program from CD Hi all,

I have been playing around with the two sources quoted in the

subject. The formulas for Rin and Ro on p 2.25 do not appear to

include any reference to the value 'C col-base' as the FBA program

does. This (I believe) leads to results for Rin and Ro that differ by

quite a bit in the examples I have tried.

Am I correct that if I did include the effect of the collector to

base capacitance in the Rf value in the formulas on p 2.25 the results

for Rin and Ro would match better to what is reported by FBA with a

given value for C col-base?

Assuming this is correct, am I also correct that the "adjusted" value

for Rf in the formulas would have to be calculated as a complex number

as it would now include real (resistor) and imaginary (capacitor)

values?

I guess my real question is how to get the two methods to agree. If

anyone is interested I can forward my circuit values.

Tnx es 72

Bob WB0POQ815 2007-06-01 11:49:41 Wes Hayward Re: AC formulas on p2.25 vs FBA program from CD Hi Bob and group,

Good question. Yes, there is a big difference between the two

evaluations for the feedback amplifier. We would expect this, for

the two cases used quite different assumptions for the analysis.

The equations in Fig 2.69 assumed an ideal transistor in the circuit

of Fig 2.63. The transistor has a beta value that holds for all

frequency. The intrinsic emitter resistance is lumped in with the

external emitter resistance of Re. I plugged some numbers into the

equations of Fig 2.69 with the following parameters:

beta=100

emitter current=20 mA and 10 Ohms degeneration for Re=11.3

Rs=50

RL=200

RF=1000

The results were Gt=18.0 dB, Rin=61.3, and Ro=202.

The analysis in FBA uses a modified hybrid pi model. See the info

in IRFD, or many other places for details on this model. It is a

small signal model that includes F-t for the transistor. The F-t is

used to generate a shunt capacitor that appears in parallel with the

emitter base junction. I did further modifications by placing a

small resistor in series with the input, called Rb'. This is the so

called base spreading resistance. A "Miller C" of a few pF is also

tacked from collector to base. Within the program, I generate the y-

parameters for this combination based upon the external emitter

degeneration (R and inductance) and an assumed standing current. The

resulting y matrix is modified with the collector to base feedback

network, which includes series R, L, and C. The termination at the

input is set while that at the output is picked by setting an overall

load and a transformer turns ratio. If we pick RL=50 and N=2 (which

is the default built into the program) we end up with 200 Ohms as the

load at the collector. The program lets the user alter F-t, beta,

Rb', and Miller C = C col-base.

I wanted to see what we would get with this analysis if we assume

parameters that might fit with the previous analysis. I picked the

following :

Transistor: beta=100, F-t=30000, Rb'=.001, Ccb=.001

F = .01

Rs=50, RL=50, N=2

Ie=20 mA, R degeneration = 10, with .01 nH inductor

Rfb=1000 with 100000000 pF and .01 nH

The analysis results are then Gt=18.01 dB, Zin=61.4+j.008, and Zout=

201.5-j.03.

Essentially, we have excellent agreement. You can now start

changing the frequency dependent parameters to see what the impact

might be.

There are a lot of things that we can do with this. You can change

the assumptions for the initial analysis and derive your own

equations to replace those of Fig 2.69. For example, what will

happen if we replace all (beta+1) terms with beta.

Another thing to do is to find some published scattering parameters

for a transistor of interest and then analyze a feedback amplifier

using them. This will take some serious arithmetic or a suitable

computer program. The old ARRL Radio Designer would do it.

Another thing to do is to use LT SPICE. The SPICE models for our

common transistors are easy to find all over the web. I'll do this

analysis and report the results here.

Bottom line: This is a game of modeling that we are playing. We

are picking models of varying complexity in order to try and predict

circuit behaviour. The transistor model used for Fig 2.69 equations

is purely scalar, so we don't encounter any complex mathematics.

This was not the case with the action that happens within FBA. If we

go deeper and become even more thorough in the mathematical models we

use for the transistors, we come closer and closer to a description

of the physical world that we would measure when we build the circuit.

I hope that this clarifies the situati816 2007-06-01 15:23:03 Wes Hayward Re: AC formulas on p2.25 vs FBA program from CD Hi all,

In a previous posting, I discussed two methods in EMRFD that address

single transistor feedback amplifiers. I just posted a PDF that

summarizes some of these comparisons and includes a SPICE analysis.

The same circuit is used for all three.

I hope this clarifies the situation.

73, Wes