Q: feedback and input impedance in a emitter follower

[Peter Andersen]

Hi there

I have a problem with some calculations regarding feedback and input
impedance on a simple one stage transistor circuit here:
http://www.mespilus.dk/Feedback_1.pdf

With the feedback circuit (R5 + C6) connected I can measure a gain of 8.85.
The input impedance is 1,08Kohm.

With the feedback circuit disconnected I get a gain of 105 and a input
impedance of 4,11Kohm.

The question is now: how is the right way to calculate these values when I'm
designing? if I use the standard formular for designing input impedance
(Zin= hie//R1//R2) I get a impedance of 1,88Kohm. If the feedbackcircuit is
going to be in parallel with R1 it will decrease to 1,6Kohm - but still not
right.

Please.... can anyone please explain how to do this right and how to
calculate the input impedance, gain and so one for this kind of circuits?

Peter

 

[Charles Schuler]

Hi there

I have a problem with some calculations regarding feedback and input
impedance on a simple one stage transistor circuit here:
http://www.mespilus.dk/Feedback_1.pdf

With the feedback circuit (R5 + C6) connected I can measure a gain of
8.85. The input impedance is 1,08Kohm.

With the feedback circuit disconnected I get a gain of 105 and a input
impedance of 4,11Kohm.

The question is now: how is the right way to calculate these values when
I'm designing? if I use the standard formular for designing input
impedance (Zin= hie//R1//R2) I get a impedance of 1,88Kohm. If the
feedbackcircuit is going to be in parallel with R1 it will decrease to
1,6Kohm - but still not right.

Please.... can anyone please explain how to do this right and how to
calculate the input impedance, gain and so one for this kind of circuits?

It is not an emitter follower ... that should help you do your homework!

 

[Peter Andersen]

It is not an emitter follower ... that should help you do your
homework!

Arhhh. your right. Sorry, that should of cause be common emitter!



BTW: nope, not homework..



Peter

 

[Charles Schuler]

The loading effect of R5 is set by the current through it ... which in this
case is larger due to the inverted signal at the collector of the transistor
(in other words, the effective value of R5 is much smaller than 10 k in the
ac equivalent circuit). That's why the input impedance drops with the
collector feedback connected. The approximations for this circuit are
simple and can be found in all the standard textbooks.

 

[Peter Andersen]

The loading effect of R5 is set by the current through it ... which
in this case is larger due to the inverted signal at the collector of
the transistor (in other words, the effective value of R5 is much
smaller than 10 k in the ac equivalent circuit). That's why the
input impedance drops with the collector feedback connected. The
approximations for this circuit are simple and can be found in all
the standard textbooks.

The standard textbooks tells me that:

Zin'=Zin/M
Zin' = inputimpedance with feedback
Zin = inputimpedance without feedback
M = Feedback factor
M = Ao/A'
Ao= openloopgain
A' = gain with feedback.

So in this case Zin is 4K, M is 11,86 and the Zin' should then be 337ohm -
which is not correct.

What is wrong here? - and what kind of standard textbooks could you
recommend me? (give me some titles). AoE doesn't cover this subject.

Peter

 

[The Phantom]

Hi there

I have a problem with some calculations regarding feedback and input
impedance on a simple one stage transistor circuit here:
http://www.mespilus.dk/Feedback_1.pdf

With the feedback circuit (R5 + C6) connected I can measure a gain of 8.85.
The input impedance is 1,08Kohm.

I don't see a C6 in your circuit; do you mean C4?

With the feedback circuit disconnected I get a gain of 105 and a input
impedance of 4,11Kohm.

The question is now: how is the right way to calculate these values when I'm
designing? if I use the standard formular for designing input impedance
(Zin= hie//R1//R2) I get a impedance of 1,88Kohm. If the feedbackcircuit is
going to be in parallel with R1 it will decrease to 1,6Kohm - but still not
right.

Please.... can anyone please explain how to do this right and how to
calculate the input impedance, gain and so one for this kind of circuits?

Do you have a spec sheet for the BC547A transistor? Is one available on the
net? And, what are the h parameters at the operating point (I assume the
circuit is operating at low, audio, freqencies; if not, what is the operating
freqency)?

Do you want to include the impedance of the capacitors in the calculations, or
do you want to assume that the caps can be taken as AC short circuits?

 

[Peter Andersen]

I don't see a C6 in your circuit; do you mean C4?

Yes, of cause! sorry.

Do you have a spec sheet for the BC547A transistor? Is one
available on the net? And, what are the h parameters at the
operating point (I assume the circuit is operating at low, audio,
freqencies; if not, what is the operating freqency)?

Yes the amp is LF. I don't have any specifications on the BC547A. It is a
simulation from Electronic Workbench 9 where hfe is held at 100.

Do you want to include the impedance of the capacitors in the
calculations, or do you want to assume that the caps can be taken as
AC short circuits?

I take them as AC shorts.



Peter

 

[The Phantom]

Yes, of cause! sorry.


Yes the amp is LF. I don't have any specifications on the BC547A. It is a
simulation from Electronic Workbench 9 where hfe is held at 100.

Are you simulating this whole circuit in Electronic Workbench 9? Are you
asking for a procedure to determine the input impedance and gain in Workbench?
Or do you want a method to calculate these just with algebra?

 

[Charles Schuler]

The standard textbooks tells me that:

Zin'=Zin/M
Zin' = inputimpedance with feedback
Zin = inputimpedance without feedback
M = Feedback factor
M = Ao/A'
Ao= openloopgain
A' = gain with feedback.

So in this case Zin is 4K, M is 11,86 and the Zin' should then be 337ohm -
which is not correct.

What is wrong here? - and what kind of standard textbooks could you
recommend me? (give me some titles). AoE doesn't cover this subject.

Are you perhaps evaluating the gain taking the input signal as that which
appears at the right end of R6 but evaluating the input impedance from the
left end of R6?

 

[Peter Andersen]

Are you simulating this whole circuit in Electronic Workbench 9?
Are you asking for a procedure to determine the input impedance and
gain in Workbench? Or do you want a method to calculate these just
with algebra?

No, It's not at problem to calculate the inputimpedance in EW9, so what I am
looking for is some algebra to do it by the hand in the designing phase
after I have calculatet the resistorvalues for this kind of circuit. As
Charles Schuler said it must be standard textbook procedure, but I can't
find any algebra and procedures anywhere that goes deeper than describing
the very simple rules about feedback (the four basic methods, etc.).

Peter

 

[Peter Andersen]

Are you perhaps evaluating the gain taking the input signal as that
which appears at the right end of R6 but evaluating the input
impedance from the left end of R6?

I dont think so. The input (left end of R6) draws 4,86uA in 20mV which gived
4,1Kohm input impedance.

But first fo all I much rather want to know the correct formulars for
calculating these things in this kind of circuit, after that we can discus
the errors. I need to know if I'm doing this right.

Peter

Peter

 

[The Phantom]

Hi there

I have a problem with some calculations regarding feedback and input
impedance on a simple one stage transistor circuit here:
http://www.mespilus.dk/Feedback_1.pdf

With the feedback circuit (R5 + C6) connected I can measure a gain of 8.85.
The input impedance is 1,08Kohm.

With the feedback circuit disconnected I get a gain of 105 and a input
impedance of 4,11Kohm.

The question is now: how is the right way to calculate these values when I'm
designing? if I use the standard formular for designing input impedance
(Zin= hie//R1//R2) I get a impedance of 1,88Kohm. If the feedbackcircuit is
going to be in parallel with R1 it will decrease to 1,6Kohm - but still not
right.

Please.... can anyone please explain how to do this right and how to
calculate the input impedance, gain and so one for this kind of circuits?

Peter

Go to this site and get the datasheet for the BC547; get the one from
Vishay because it has h parameters:
http://www.datasheetcatalog.com/datasheets_pdf/B/C/5/4/BC547A.shtml

The DC collector current in your circuit is around 1.15 mA. The
datasheet gives the h parameters (at 1 KHz) on pages 2 and 3 for a
collector current of 2 mA. This transistor is available in 3 hfe groups.
The lowest hfe for which the h parameters are given is 220. I extrapolated
the parameters down to hfe = 100. Then using the curves in Figure 8, I
adjusted the parameters for a collector current of 1 mA. My final numbers
are:

hie = 1800
hfe = 100
hre = .00015
hoe = 6 * 10^-6

Another person might get slightly different numbers, but these are good
enough for a reasonable analysis. The analysis I performed is a nodal
analysis. It doesn't make any approximations for feedback, but it can be a
bit complicated. However, with modern mathematical software, the math is
done for you; the hardest part is getting it set up correctly. In fact,
once you have it set up, you can do the matrix math on a calculator. I've
posted the analysis over on alt.binaries.schematics.electronics with the
subject line "Andersen circuit analysis". Unzip it into a temp folder and
double click the index file. It should open in your browser.

With these values and with feedback, I get an input impedance of 1054.2
ohms, and a gain of -9.12

Without feedback, I get an input impedance of 2596 ohms, and a gain of
-160.5. If I change hie to 3750 ohms, and hfe to 111, I get an input
impedance without feedback of 4111 ohms and a gain of -105.3, closer to
your measured (I think) values.

The results without feedback are sensitive to the actual h parameters of
the transistor, of course.

 

[Eeyore]

Go to this site and get the datasheet for the BC547; get the one from
Vishay because it has h parameters:
http://www.datasheetcatalog.com/datasheets_pdf/B/C/5/4/BC547A.shtml

The DC collector current in your circuit is around 1.15 mA. The
datasheet gives the h parameters (at 1 KHz) on pages 2 and 3 for a
collector current of 2 mA. This transistor is available in 3 hfe groups.
The lowest hfe for which the h parameters are given is 220. I extrapolated
the parameters down to hfe = 100. Then using the curves in Figure 8, I
adjusted the parameters for a collector current of 1 mA. My final numbers
are:

hie = 1800
hfe = 100
hre = .00015
hoe = 6 * 10^-6

And you reckon you need these for a simple analysis ?

Sheesh !

Graham

 

[Eeyore]

Hi there

I have a problem with some calculations regarding feedback and input
impedance on a simple one stage transistor circuit here:
http://www.mespilus.dk/Feedback_1.pdf

That's a horrid circuit btw. I hoped I'd seen the last of that kind of thing in
the late 70s. Why on earth are you using such a thing ?

Graham

 

[Eeyore]

Please.... can anyone please explain how to do this right and how to
calculate the input impedance, gain and so one for this kind of circuits?

What input imedance and gain do you actually want ? Do you actually want it to
be inverting ? If not, I can improve the noise figure too while I'm at it.

Graham

 

[Eeyore]

I dont think so. The input (left end of R6) draws 4,86uA in 20mV which gived
4,1Kohm input impedance.

But first fo all I much rather want to know the correct formulars for
calculating these things in this kind of circuit, after that we can discus
the errors. I need to know if I'm doing this right.

You're worrying too much about formulas.

OTOH if you had a firm grasp of practical ( as opposed to theoretical ) circuit
theory you wouldn't need to worry about them !

Frankly this is more of 'back of a cigarette packet' job.


Graham

 

[Eeyore]

What input imedance and gain do you actually want ? Do you actually want it to
be inverting ? If not, I can improve the noise figure too while I'm at it.

Correction. It would still be invertsing but using series feedback instead of
shunt so the input Z goes up and the noise goes down.

Graham

 

[Eeyore]

The question is now: how is the right way to calculate these values when I'm
designing? if I use the standard formular for designing input impedance
(Zin= hie//R1//R2) I get a impedance of 1,88Kohm. If the feedbackcircuit is
going to be in parallel with R1 it will decrease to 1,6Kohm - but still not
right.

Your analysis is so far wrong I can't imagine where you got that idea.

R6 is the dominant term in the input impedance in that circuit.

Graham

 

[Eeyore]

The standard textbooks tells me that:

Zin'=Zin/M
Zin' = inputimpedance with feedback
Zin = inputimpedance without feedback
M = Feedback factor
M = Ao/A'
Ao= openloopgain
A' = gain with feedback.

So in this case Zin is 4K, M is 11,86 and the Zin' should then be 337ohm -
which is not correct.

What is wrong here?

Absolutely everything !

- and what kind of standard textbooks could you
recommend me? (give me some titles). AoE doesn't cover this subject.

Where did you get these 'standard equations' ???? They're nonsense.

Incidentally the actual numbers are fairly free of the influence of h
parameters. For this simple kind of circuit you can assume almost any small
signal transistor to be 'the same' within reason.

Graham

 

[Eeyore]

I take them as AC shorts.

The first sensible advice I've seen so far in this thread !

Graham