# Question about “dominant capacitor” in filter circuits

#### FuneralHomeJanitor

Joined Oct 12, 2019
54
I am having trouble understanding the term “dominant capacitor” used in the book for filter circuits and frequency responses of amplifiers. This is all my book says on it and it is not very descriptive. What makes it more important than the others in a circuit like a common emitter amplifier? How is it determined? Thanks in advance.

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#### crutschow

Joined Mar 14, 2008
34,847
A "dominant capacitor" would be the one that primarily determines the rolloff characteristics of the filter (not every filter will have one).
The other capacitors will then have only a small or perhaps no effect on that rolloff.

#### Ian0

Joined Aug 7, 2020
10,277
The criterion for stability in an amplifier (any amplifier) is that the gain falls below unity at a LOWER frequency than the phase shift reaches 180 degrees.
To achieve this the "dominant pole capacitor" reduces the open-loop gain at 6dB/octave, starting at a very high open-loop gain at a very low frequency. It is "dominant" because it makes sure that the gain reaches unity before any other poles and zeroes from any other parts of the amplifier, or the load, have any effect - in theory. In practice, there is nearly always a customer somewhere who can find a load with such a weird frequency response that sends the amplifier unstable.
This is the graph from the TL071 op-amp. The gain slope is due to its internal dominant pole capacitor. You can see that the gain crosses 1 just before the phase shift reaches 180 degrees. The phase shift remains at 90 degrees throughout much of the frequency range - this is the effect of the dominant pole capacitor. The transition from 90 degrees to 180 degrees is due to the influence of the other poles. The dominant pole is "dominant" because it manages to get the gain down to 1 before the other poles can possibly send it unstable.

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#### LvW

Joined Jun 13, 2013
1,778
(1) An operational amplifier which has the task just to amplify must be stable for all kinds of resistive feedback.
For this purpose, the opamp unit must be unity-gain compensated using a "dominant pole" (caused by a "dominanat capacitor") . This case was discussd in the above contribution (Ian0)
(2) But your question concerns an active circuit to be used as a filter! To illustrate your example you show an equation that belongs to a 2nd-order BANDPASS.
In such a case, there is only one capacitor which primarily determines the lower cut-off frequency - and another capacitor which is primarily responsible for the upper cut-off frequency.
(3) However, for higher-order filter circuits, it is not possible - and not necessary - to identify a "dominant" capacitor. For realization of a desired transfer function ALL the parts are responsible.
(4) For some other feedback systems (control theory) it can happen that there are, for example, two poles which are not very close to each other. Only in such a case, we can identify a "dominant" pole (caused by a "dominant" capacitor).

#### WBahn

Joined Mar 31, 2012
30,303
I am having trouble understanding the term “dominant capacitor” used in the book for filter circuits and frequency responses of amplifiers. This is all my book says on it and it is not very descriptive. What makes it more important than the others in a circuit like a common emitter amplifier? How is it determined? Thanks in advance.
First, let's begin with the notion that at very low frequencies all capacitors in the circuit will behave like open circuits and at very high frequencies they will all behave like short circuits.

Next, let's assume (it's a good assumption for most circuits, but not guaranteed) that within the midband of the circuit all of the capacitors are either pretty firmly acting like opens or pretty firmly acting like shorts. If not, then it is very difficult to have a reasonable constant gain as the frequency changes within the midband.

Now imagine that you are parked in the middle of the midband. As you lower the frequency nothing will happen for a while, but at some point at least one of the capacitors that has been acting like short will transition to acting like an open. The result will be a change in gain. When this happens, then if only one capacitor is making this transition, that capacitor is the dominant capacitor setting the lower cutoff frequency and the rolloff will be a first-order rolloff. The same happens as you increase the frequency until one or more capacitors transition from behaving like opens to shorts. If more than one capacitor is involved with either transition out of the midband, then you don't have a first order rolloff and this doesn't apply.

#### Ian0

Joined Aug 7, 2020
10,277
Now imagine that you are parked in the middle of the midband. As you lower the frequency nothing will happen for a while, but at some point at least one of the capacitors that has been acting like short will transition to acting like an open. The result will be a change in gain. When this happens, then if only one capacitor is making this transition, that capacitor is the dominant capacitor setting the lower cutoff frequency and the rolloff will be a first-order rolloff. The same happens as you increase the frequency until one or more capacitors transition from behaving like opens to shorts. If more than one capacitor is involved with either transition out of the midband, then you don't have a first order rolloff and this doesn't apply.
Good explanation, but have you actually come across the term "dominant capacitor" being used in any other context than "dominant pole capacitor"?

#### WBahn

Joined Mar 31, 2012
30,303
Good explanation, but have you actually come across the term "dominant capacitor" being used in any other context than "dominant pole capacitor"?
No. I've only seen this approach referred to as "dominant pole", but referring to the capacitors that establish that pole as dominant capacitors seems pretty reasonable and I wouldn't be at all surprised if I referred to them that way when I was teaching this stuff (gee, has it really been twenty years ago?). We usually think in terms of band-pass filters, but the concept should apply equally to band-reject filters in which case they would be dominant zero capacitors.

#### sparky 1

Joined Nov 3, 2018
786
Electronic principals by Malvino and Bates chapter 14-1

"in an amplifier where there is one dominant capacitor producing the lower cutoff frequency..."

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#### Ramussons

Joined May 3, 2013
1,418
I am having trouble understanding the term “dominant capacitor” used in the book for filter circuits and frequency responses of amplifiers. This is all my book says on it and it is not very descriptive. What makes it more important than the others in a circuit like a common emitter amplifier? How is it determined? Thanks in advance.
The attachment explanation relates to amplifiers.
In any amplifier, there are Coupling Capacitors and Bypass capacitors. The Cutoff Frequency for each will depend on the Resistive Coupling that exists. (i take it that there are no Inductors in the amps).
What the author talks about is the "weakest" coupling that determine the End points of the amplifier pass band.
For example, if there are 3 similar amplifier stages with coupling capacitors of 1 uF, 0.5 uF and 0.1 uF, the Dominant Capacitor for the Low frequency end is the 0.1 uF. It is like having a 1 uF capacitor at the amp Line In, a 1000 uF at the speaker Out, but a 1 nF somewhere in the interstage coupling. That 1 nF becomes the Dominant capacitor for Low frequency.
Similarly, one can locate the Dominant capacitor for the High Frequency Cut off.
It is these Dominant capacitors that determine the Amplifier Frequency response.