I have a problem with some calculations regarding feedback and input impedance on a simple one stage transistor circuit here:
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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?
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.
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.
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?
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?
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?
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.).
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.
Go to this site and get the datasheet for the BC547; get the one from Vishay because it has h parameters:
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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.
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.
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.
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