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Analog filter delay time

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mordak

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Hi,

I am trying to design an analog low pass filter. I was wondering if there is any equation showing the relation between the filter spec, say order of the filter, and its settling time and propagation delay. And if there is any, will it depend on the filter topology?

Any help is appreciated!
Thanks
 

The delay time of an lowpass RC filter is the phase shift that can be calculated. Of course if the filter has more RC's in it for a higher order then the phase shift and delay are
more.
 

mordak said:
will it depend on the filter topology?

Any help is appreciated!
Thanks
Click to expand...

A capacitor filter will advance/ delay a signal, in the opposite direction from its sister inductive filter.

- - - Updated - - -

I find my reply is not correct, or not always. I'm getting a refresher as I compare simulations of RC and RL high pass filters with the same rolloff curve.
 

BradtheRad said:
A capacitor filter will advance/ delay a signal, in the opposite direction from its sister inductive filter.
Click to expand...
"opposite direction" - do you think inductive filters will produce a NEGATIVE delay?
 

Audioguru said:
The delay time of an lowpass RC filter is the phase shift that can be calculated. Of course if the filter has more RC's in it for a higher order then the phase shift and delay are
more.
Click to expand...
Thanks Audioguru for your reply. Would you mind sending me a ref that has those equations?
I am aware that say a first order low-pass filter needs some time based on its time constant to settle properly. However, I am looking for a quantitative way to figure out the propagation delay and settling time for filters based on the order. Say if I have a 7th-order filter, I want to know how long I need to wait until I get the valid output. Besides, at the moment I am not sure if this delay time is topology dependent or not.

BradtheRad said:
I find my reply is not correct, or not always. I'm getting a refresher as I compare simulations of RC and RL high pass filters with the same rolloff curve.
Click to expand...
LvW said:
"opposite direction" - do you think inductive filters will produce a NEGATIVE delay?
Click to expand...
Thanks BradtheRad and LvW for your comments, I would be happy to have your opinions on this as well.

Thanks!
 

LvW said:
"opposite direction" - do you think inductive filters will produce a NEGATIVE delay?
Click to expand...

The basic principle says 'inductors lag current, capacitors lead current'. However by tapping at different spots for output voltage, we can get various effects. It requires placing components in the right places, and experimenting with values.

This illustrates how to get voltage advance (NEGATIVE delay) in an inductive low pass filter.

5122858500_1470326731.png


------------------------------

Edit: However by taking V output ahead of the inductor, you get a high pass filter. The phase shift advances, attenuating low frequencies (in a manner that still is hard for me to get my head around). This is the definition of a filter and it creates the rolloff curve.
 

mordak said:
I am aware that say a first order low-pass filter needs some time based on its time constant to settle properly. However, I am looking for a quantitative way to figure out the propagation delay and settling time for filters based on the order. Say if I have a 7th-order filter, I want to know how long I need to wait until I get the valid output. Besides, at the moment I am not sure if this delay time is topology dependent or not.
Click to expand...

mordak - you must clearly distinguish between (a) settling time and (b) delay resp. group delay of a filter circut.
So - what are you interested in?
 

mordak said:
Thanks Audioguru for your reply. Would you mind sending me a ref that has those equations?
I am aware that say a first order low-pass filter needs some time based on its time constant to settle properly. However, I am looking for a quantitative way to figure out the propagation delay and settling time for filters based on the order. Say if I have a 7th-order filter, I want to know how long I need to wait until I get the valid output. Besides, at the moment I am not sure if this delay time is topology dependent or not.
Click to expand...
An RC lowpass filter cuts high frequencies. One RC produces a maximum phase shift delay of 90 degrees that is simply calculated from the frequency that is fed to it. It has no settling time but since high frequencies are reduced then the rise and fall times of transients are slowed.
Active filters sharper than Bessel have ringing on transients that has a settling time.
 

Audioguru said:
An RC lowpass filter cuts high frequencies. One RC produces a maximum phase shift delay of 90 degrees that is simply calculated from the frequency that is fed to it. It has no settling time but since high frequencies are reduced then the rise and fall times of transients are slowed.
Active filters sharper than Bessel have ringing on transients that has a settling time.
Click to expand...

I doubt if we can say that a phase shift is identical to a delay. A delay is given in seconds - and not in degree. Delay is given in seconds and not in degree!
More than that, for a simple RC stage the max. phase shift of 90 deg does exist for INFINITE frequencies only (that means: it will never be reached in reality).
Of course, even the first order RC block has a settling time.

@ mordak: What do really need to know?
 

If the frequency is 1kHz and the phase shift is 45 degrees then the delay is (1/1000Hz) x (45 degrees/360 degrees)= 125us.
 

LvW said:
I doubt if we can say that a phase shift is identical to a delay. A delay is given in seconds - and not in degree. Delay is given in seconds and not in degree!
More than that, for a simple RC stage the max. phase shift of 90 deg does exist for INFINITE frequencies only (that means: it will never be reached in reality).
Of course, even the first order RC block has a settling time.

@ mordak: What do really need to know?
Click to expand...

Audioguru said:
If the frequency is 1kHz and the phase shift is 45 degrees then the delay is (1/1000Hz) x (45 degrees/360 degrees)= 125us.
Click to expand...

Thanks for the comments. I included a figure form an online article about filters:


I am interested in both propagation delay and settling time, but mostly propagation delay. Let's say you have a sine wave that at the time t=0 you apply the signal to the circuit. The output of the filter at t=t1 becomes valid, so the filter is able to catch up with the signal and follow the input signal (with some phase shift). So this dead zone (propagation delay) where the output of the filter is not valid between t=0 and t=t1 is of my interest. Of course if you run the circuit for a couple of periods you will only see the phase shift between the input and output signals.
Besides, I think phase of the filter is independent from the filter order (in some cases). You may have a linear, non-linear, and zero phase shift filters with the same order.
 

You show a digital pulse where the source is saturated (not linear) so the propagation delay is caused by the source device coming out of saturation. A linear circuit responds immediately but has a slow slew rate caused by a lowpass filter in it. Positive feedback at high frequencies causes the ringing shown. Some active lowpass filters types use too much positive feedback to produce a sharp cutoff but it causes some ringing.
 

Audioguru said:
You show a digital pulse where the source is saturated (not linear) so the propagation delay is caused by the source device coming out of saturation. A linear circuit responds immediately ......
Click to expand...

Sorry, but this is not correct.
Each filter needs a certain "transient" time before it behaves as desired (filter action).
This time depends on the filter degree as well as on the Q value of the pole pair(s).

Example: This finite transient time (in german: Einschwingzeit) is the reason for the finite search velocity of an analog spectrum analyzer.
When you increase the resolution (smaller bandwidth, larger Q) you must at the same time reduce the search velocity because the search filter (bandpass) needs time to correctly respond to the signals.
 
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The term slew rate seems to refer to non-linear amplifier behavior, in so far Audioguru's comment is substantiated. A linear filter doesn't show slew-rate, but the pulse response might look quite similar to the post #11 picture though.

A common way to describe the frequency dependent delay respectively phase shift of a linear filter is the group delay. It has a well defined characteristic for specific filter prototypes.
 

mordak said:
Hi,

I am trying to design an analog low pass filter. I was wondering if there is any equation showing the relation between the filter spec, say order of the filter, and its settling time and propagation delay. And if there is any, will it depend on the filter topology?

Any help is appreciated!
Thanks
Click to expand...

I agree with FVM

Slew rate , defined only for large signals is current limited by Ic= Cdv/dt and becomes non-linear with saturation affecting current gain on bipolar devices.
Group delay is the rate of change of phase shift which is not flat in most filters.
Maximally flat group delay filters are called Bessel https://en.m.wikipedia.org/wiki/Bessel_filterFilters.
THere are many other filter names for max. flat amplitude, equal ripple, minimum phase shift etc.

For communications, zero intersymbol phase shift in binary encoders uses a "raised cosine filter" for zero ISI. https://en.m.wikipedia.org/wiki/Intersymbol_interference.

https://en.m.wikipedia.org/wiki/Raised-cosine_filter

For a BW limited scope of say 300MHz, it has a linear rise time of just under 1ns, thus for their filter, BW=1/(3.3 * Tr)
 
Last edited:

Gentlemen - why do you speak about the slew rate? I am afraid, this will puzzle the OP.
He is just asking for delay properties of an anlog filter - thats all.
 

LvW said:
Gentlemen - why do you speak about the slew rate? I am afraid, this will puzzle the OP.
He is just asking for delay properties of an anlog filter - thats all.
Click to expand...
He showed a pulse. The slew rate affects its rise-time and fall-time.
 

Thanks all for the responses. I really appreciate your help.

LvW said:
Sorry, but this is not correct.
Each filter needs a certain "transient" time before it behaves as desired (filter action).
This time depends on the filter degree as well as on the Q value of the pole pair(s).
.
Click to expand...
Do you know any ref that formulates these relationships?

Audioguru said:
He showed a pulse. The slew rate affects its rise-time and fall-time.
Click to expand...

FvM said:
The term slew rate seems to refer to non-linear amplifier behavior, in so far Audioguru's comment is substantiated. A linear filter doesn't show slew-rate, but the pulse response might look quite similar to the post #11 picture though.

A common way to describe the frequency dependent delay respectively phase shift of a linear filter is the group delay. It has a well defined characteristic for specific filter prototypes.
Click to expand...

LvW said:
Gentlemen - why do you speak about the slew rate? I am afraid, this will puzzle the OP.
He is just asking for delay properties of an anlog filter - thats all.
Click to expand...

I think the propagation delay is related to the filter order. There is also slewing in the figure I posted and I think it comes from the opamp used in the filter, actually the reference I posted this figure from, also talks about the slewing.

Though the ref mentions that : "The propagation delay time is the inverse of the phase (Figure 3) of the fundamental of the input signal, still I am not quite clear, since I thought the propagation time depends on other things.
 

Group delay is the time delay of the amplitude envelopes of the various sinusoidal components of a signal thru a filter or device
Just for a filter Group Delay = dφ/df or the slope of phase vs f which depends on the type of filter, and the order.

Phase delay is the time delay = %phase shift x Tf which applies to only 1 frequency of period = Tf

In general, Phase "shift" can be either an inversion or a propagation delay or a group delay
 
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mordak said:
I think the propagation delay is related to the filter order.
Click to expand...

I like to watch this simulation because it turns me on my head. It makes it hard to think in terms of propagation delay. The output advances ahead of the source sinewave! It advances immediately within a cycle after powerup.

9075958500_1470461767.png


Each RC stage has a time constant, creating a certain amount of advance. The advance is greatest at slower frequencies.

If you want more advance, then you must accept a smaller output waveform. There is a formula showing the relationship.

By adding more RC stages you can advance the output even more. I have a simulation with 16 stages. The output is more than 2 sine cycles earlier than the source.
 
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