# Low and High Frequnecy Response

1. ## Low and High Frequnecy Response

Why do we use RC time constants to get the high and low frequency response? What is the physical explanation behind this ?

2. ## Re: Low and High Frequnecy Response

Hi,

What context?

Klaus

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3. ## Re: Low and High Frequnecy Response

First, my apologies for a confusing questions. I will try to be specific.

For example: We use OCTC ( Open circuit time constant method ) to get the high frequency response for amplifiers. I understand the Maths about dominant pole approximation and how WH= 1/tau(j). where j is the number of high frequency caps in the circuit.
what I do not follow: How is the time constant of a capacitor related to a high frequency response of amplifier ? How would you explain this in a simple manner.

I hope I was clear this time.

Thank you.

4. ## Re: Low and High Frequnecy Response

In other words , what is the relationship between bandwidth and Time constant ?

5. ## Re: Low and High Frequnecy Response

In the simplest case an amplifier can be viewed as an R and C circuit, say for simplicity 1st order R-C. For example R being the resistance looking into the output of the amplifier (Thevenin resistance) and C - equivalent load capacitance.
If we apply higher and higher frequency to that circuit, we would need to charge the capacitor faster and faster, that is use more and more current for that. The resistor though would limit the amount of current and thus impose limitation on how fast we can move the output. This is kind of hand wavy explanation. Math says that the -3db frequency is 1/RC for that 1st order circuit.

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6. ## Re: Low and High Frequnecy Response

Also, when we are doing the high frequency response, the dominant pole should not be at the output ? Why?

For example in a single stage cascade structure, the dominant pole lies at the output. Why is this not good ?

7. ## Re: Low and High Frequnecy Response

There is no such rule that the dominant pole can't be at the output.
It is not about being cascoded or not. It is more about being 1 stage amplifier vs. two stage. You remember that all we want to have for a stable negative feedback amplifier is the loop gain crossing 0dB with a -20db/dec i.e. like a 1 pole response. In a 1 stage cascoded amplifier which has at least 2 poles, the non-dominant pole is at the cascode transistor source and is usually at some fraction of ft of the technology. Since it is at such relatively high frequency and is more or less fixed, it is very easy to compensate the loop by just having enough load capacitance at the output and thus making the loop gain -20db/dec at the cross-over frequency.
In two stage amplifiers situation is a bit different. There the two poles of the open loop amplifier (one at the 1st stage output and another one at the second stage output) could be quite comparable in value. In this case it is better to use Miller compensation because it just does what we want - pole splitting. It pushes the dominant pole at the output of the 1st stage towards low frequencies and pushes the non-dominant pole at the output of the second stage towards high frequencies.
Now, if in the case of a two stage amplifier you drive a very low load capacitance, so that the 2nd stage pole is at high frequencies, then you can still use load compensation, connecting more cap at the output of the 1st stage and thus making the loop gain cross 0dB with 20db/dec. Or vice versa - if for some reason the 1st stage loading is very small, then you can connect more cap at the output of the 2nd stage and still have -20dB/dec crossing. But in the general case this are not optimum solutions for a two stage amplifiers.

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8. ## Re: Low and High Frequnecy Response

How can you tell that a particular circuit has n number of poles without doing any calculation? you mentioned ,"In a 1 stage cascoded amplifier which has at least 2 poles, the non-dominant pole is at the cascode transistor source " How do you know that another pole is at the source of Cascode transistor ? All the device capacitances ( even caps at the source of cascode stage )contributes to a dominant pole.

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9. ## Re: Low and High Frequnecy Response

How do you know that another pole is at the source of Cascode transistor ?
By sketching and analysing the equivalent circuit of the amplifier.

All the device capacitances ( even caps at the source of cascode stage )contributes to a dominant pole.
No, no. The first and second stage clearly constitute separate poles (at least two, as stated) which can't be summed up to a single pole. An single pole has 90° asymptotic phase lag, a double pole 180°. But the second, non-dominant pole becomes effective in the higher or even above the used frequency range of the amplifier.

10. ## Re: Low and High Frequnecy Response

"No, no. The first and second stage clearly constitute separate poles (at least two, as stated) which can't be summed up to a single pole. An single pole has 90° asymptotic phase lag, a double pole 180°. But the second, non-dominant pole becomes effective in the higher or even above the used frequency range of the amplifier."

I do not follow this. Lets say the output node is O, the input node is I and the intermediate node i.e. input of cascode stage or the output of input stage is labeled as X.. From OCTC ( open circuit time constant ), the dominant pole is :

WH=1/(CO RO +CI RI +CX RX) where CO represents the total capacitance at the output node, CI = total capacitance at the input node and CX= total Caps at the intermediate node. This WH has 90 degree phase lag .. Right ? According to this the capacitances at the node X do participate in the dominant pole .. Right ?

11. ## Re: Low and High Frequnecy Response

O.K., I understand what you mean. fH obtained from the said "open circuit time constant" method is an estimation of the upper 3 dB corner. It's a simplified analysis assuming a first order circuit, but not the calculation of the dominant pole.

12. ## Re: Low and High Frequnecy Response

In general, every node has a driving resistance and an equivalent capacitance and both of these form the timeconstant of that node. It is pretty easy to figure out which pole is dominant and which not if the nodes are decoupled from each other. For example, the pole at the output of the first stage can be though of as not interacting i.e. decoupled from the pole at the output of the 2nd stage. Then you know that you have two poles, one of which is lower in frequency than the other or we call it dominant. In the case of a cascode with certain approximations we can think also of decoupled poles. The source of the cascode device is low ohmic, because you have 1/gm impedance there (if the drain of the casocde is not connected to very high ohmic circuit). So, caps from the source of the cascode to gate, bulk and other nodes perhaps can be though of as being connected to ground and they form a pole there together with the 1/gm of the cascode.
Sometimes or often times it is not so simple. Nodes are interacting with each other and their driving resistances take part in the poles of each of the interacting nodes. The OTC is just an approximation, a way out of this more complex situation which limits itself only to first order timeconstants. But in fact things are more complicated than this.

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