# RC networks

Discussion in 'General Electronics Chat' started by bobbyk, Jun 13, 2006.

1. ### bobbyk Thread Starter Member

Jun 13, 2006
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In a 3-terminal linear RC passive network for sinusoidal input what is the maximum voltage gain that can be acheived? And in particular, can the voltage
gain be greater than 1?

2. ### hgmjr Moderator

Jan 28, 2005
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A gain of unity is all that you can squeeze out of a passive RC integrator circuit.

hgmjr

3. ### Papabravo Expert

Feb 24, 2006
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Passive circuits with real components cannot even have a gain of 1. There is always somne loss.

Jun 13, 2006
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5. ### bobbyk Thread Starter Member

Jun 13, 2006
12
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Can you prove that? Because I have a passive 3-terminal RC network with a voltage gain of 1.03! I'd sure like to see your proof!

Look, we're asking about VOLTAGE gain (output voltage/input voltage) for
sinusoidal steady-state input. Please reconsider your answer.

bobbyk

6. ### BladeSabre Senior Member

Aug 11, 2005
105
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An ideal RC network cannot have a gain of more than 1. You need an LCR network for that- I guess a gain of 1.03 could be caused by stray inductance in your circuit.

7. ### mozikluv AAC Fanatic!

Jan 22, 2004
1,437
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hi,

just curious, how did you arrive at a result of 1.03?

8. ### Papabravo Expert

Feb 24, 2006
10,340
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I don't have to reconsider my answer, in fact I stand by it. You on the other hand can believe whatever you want. Let me know when they award you the Nobel. I'll buy you a draft.

9. ### hgmjr Moderator

Jan 28, 2005
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bobbyk,

Papabravo has a good point. In the real world a passive RC network is bound to have some losses and so a gain of one is not actually obtainable. I should have qualified my earlier response as being based on an ideal RC circuit.

Like mozikluv, I think it would be helpful if you could describe how you arrived at your figure of 1.03.

hgmjr

10. ### mozikluv AAC Fanatic!

Jan 22, 2004
1,437
1

hi hgmjr,

quite a long time that i have participated again.

as to the above figures, i would wryly say the best that can be achieved is something like 0.98 all things considered like tolerance and variances and at an ideal condition.

mozikluv

11. ### hgmjr Moderator

Jan 28, 2005
9,030
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Welcome back mozikluv.

As to the forum topic, mozikluv's estimate of 0.98 is certainly a reasonable real world upper limit. There are a number of stray components that can contribute to the loss in a passive circuit. bladesabre's mention of inductance is just one example. In addition to stray inductance there is always leakage current in the capacitor.

One thing that should also be considered is the accuracy of the measurement equipment. Digital voltmeters and oscilloscopes all have measurement tolerances that must be considered when using them to make ultra precise measurements. And while on the subject of tolerances, there are also tolerances associated with the resistor and capacitor that make up the circuit. Just because the resistor is marked as a 10K ohm resistor does not mean that it is precisely 10K. A 5% 10K resistor can range from 9.5K to 10.5K. Likewise the capacitor will have a tolerance on it as well. These component tolerance must be considered in the measurement/calculation of the gain of the RC circuit under discussion.

I generally interpret the term "passive" when used to describe an electronic component as a way of emphasizing the fact that the component does not contribute energy to the circuit. If any circuit provides a net increase in energy as in the case of bobbyk's circuit and it is not a measurement/tolerance anomally then it must be coming from some source other than the passive components that make up the circuit.

I look forward to hearing more from bobbyk on the makeup of the circuit and how he obtained the 1.03 figure for its gain.

hgmjr

12. ### radiosmoke Member

May 30, 2006
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Would a magnetic amplifier (or is a Mag-Amp a different beast?) also have no gain other than approaching unity?
Or Can you have voltage gain and current loss, and current gain and voltage loss?
I haven't the foggiest, just a curiosity.

13. ### kubeek AAC Fanatic!

Sep 20, 2005
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Transformers amplify the mains current, while reducing the voltage. As I remember some microphones used a special transformer to increase the S/N ratio.

14. ### BladeSabre Senior Member

Aug 11, 2005
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I did not get the impression that bobbyk's circuit necessarily showed a net increase in energy. The transformer example is a good one. And I was suggesting that the stray inductance may be able to cause a voltage gain of more than 1 (rather than as a source of loss). I'm not sure if that's right, and trying to visualise what would happen, it's coming out very weird. I know it's best not to trust my intuition with this stuff and just do the math. I'll come back to this later.

Edited to add: OK, some math later, I don't think that's going to happen with the tiny values of inductance that you'd find in a circuit by accident. Put a larger inductor in there and the voltage across the capacitor can go above the supply voltage, but not in this case I don't think =P

15. ### kubeek AAC Fanatic!

Sep 20, 2005
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I think it´s just error of measurement.

16. ### BladeSabre Senior Member

Aug 11, 2005
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I think so too, at this point.

17. ### hgmjr Moderator

Jan 28, 2005
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In the absense of additional details on bobbyk's circuit and his measurement method, I agree with kubeek and bladesabre that the gain anomaly most likely can be traced to a measurement error.

hgmjr (700)

Jun 13, 2006
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19. ### bobbyk Thread Starter Member

Jun 13, 2006
12
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All your comments on precision, tolerances, etc. are interesting (and well known)
but have no bearing on my question. I'm talking about IDEAL components
and not a MEASURED network but a CALCULATED one!

I didn't claim my circuit had an "energy gain", just an open-circuit VOLTAGE gain.

20. ### hgmjr Moderator

Jan 28, 2005
9,030
214
Can you post your calculations so that we can see how you arrived at the value of 1.03?

hgmjr