Why so much difference in LC values?

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TerryG

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Joined 2005
#1
I have wondered this before but never was really curious enough to want to search out an answer. Why from one class D amp to the next, the values of the output LC section, the combination of capacitor and inductor, are so different? If all they do is filter out the RF frequency, then why are they so different from one amp to the next in design. My first inclination is to think that it is because of the impedance of the circuit they are in, primarily the output devices, but if they are working as switches this doesn't make total sense to me. I mean one way they look closed, and one way they look open, if they have no impedance of their own, then they are reflecting the impedance of the circuit before them. Anyway I just want to understand why they are so different. To me it would make sense to design a circuit so that you need very little in the way impedance with the inductor, and a larger amount of capacitance in the LC circuit, as this would make things easier.
 
#3
The values of the inductor and capacitor determine not only the cutoff frequency but also the quality factor of the filter. Designers can play with the values until they find the right combination of parameters they want (cutoff frequency, Q, physical part size, cost, etc.).

I know the Tripath data sheets for most of the their chips include equations which will allow you to calculate the output filter's cutoff frequency and Q for whatever inductor and capacitor values you want.
 
#8
As BWRX said, the values determine the Q and freq. So there is really only one value that gives you a specific cutoff with a specific rolloff into a given frequency. For instance, if an amp is supposed to operate into 8 and 4ohm loads, then you'd be best to set your critical damping [Q=0.707] at 6ohm. Then you need to set your cutoff freq at, let's say 20kHz. There is only one set of L and C values that satisfy both criteria. And since some amps, like Tripath's, use higher cutoffs they can use smaller inductors for the same Q as a lower cutoff L and C values. Get it?

I am attaching a spreadsheet I made to calculate L and C values. It needs the values of the L and both the C to ground and the C across the load. If you only have one of the other just enter a 0 in the blank. All values are per side.

For reference, the equations are:

f = 1/ (2 * pi() * sqrt( L * C))

Q = R * sqrt(C/L)
 

Attachments

#9
For the coil design, there is a small program from Micrometals that is very helpful.
Download it at www.micrometals.com

You have to use the "analysis" button, insert the core reference (for example, T106-2), wire size, number of turns, etc.
I use it regularly, but I have some doubts, perhaps someone can solve them:
-What should I input as "DC bias current" in a half-bridge case? I assume you should enter the maximum RMS output current, Irms=sqrt(Pout/R). Is this correct?
-And the "peak inductor voltage"? What's the equivalent value, the supply voltage (for example, 60V for +/-60V supply?)
-And what about the "DC output voltage", is that the maximum RMS output voltage (Vrms=sqrt(Pout*R)), the peak one or what?

Some of these values are used only to calculate losses, but they are also very useful, so having this clear could lead to a very robust design. It even plots the L vs. I curves, etc.
 
#10
Wow! that calculator has been very helpful for me rapping my brain around this. Thank you very very very much!!

But why do we want a Q value equaling .707? Why is this considered "critical damping"? What is it about that number that makes it ideal?

When I plug in the numbers for the Tripath TA2021B's values, I come up with a Q=.87178 (and f=73025.3Hz). Is there a tolerance that I don't know about? Also what are the effects if your not right on the money, what happens the further you get from Q=.707, in both directions?

I messed with this to see what I could do to get the chokes value lower, and speaker impedance made a large difference. In fact the amp3 (Tripath TA2021B chip test circuit) is spec'd for 4 ohm speakers, and with 8 ohm Q=1.74356, and if you adjust the C to ground like Tripath says to .22uf, then you get Q=1.2. this seems less than ideal based on your suggested value of Q=0.707. With 8 ohms it appears you need to increase the value of the choke to 25mH, as well as reduce C to ground to .22uf, the cut off frequency changes marginally.

Terry😎
 
#11
The difference in some filters is due to textbook calculation based on standard LRC assumptions.

In reality, the speaker is not an 8 ohm resistor. Its rising impedance will cause peaking near 20kHz which sounds nasty.

If flat response to 20kHz is desired, then the values must be tweaked a bit.

Another reason for the difference is they algorithim used, that is, Butterworth, Chebyschev, Bessel, etc.
 
#12
thespeakerguy said:
The difference in some filters is due to textbook calculation based on standard LRC assumptions.

In reality, the speaker is not an 8 ohm resistor. Its rising impedance will cause peaking near 20kHz which sounds nasty.

If flat response to 20kHz is desired, then the values must be tweaked a bit.

Another reason for the difference is they algorithim used, that is, Butterworth, Chebyschev, Bessel, etc.
Click to expand...


This doesn't make a whole lot of sense to me for the following reasons. 1) I inputed the recomended values of Tripath. 2) The cut off frequency was way above 20K Hz, something like 73K Hz. 3) We all understand the behavior of speakers, what I want to understand is how to figure LC values of the output of a class D amp, and why a Q=0.707? 4) Knowing how speakers have impedance spikes at various frequencies doesn't help, as the best we could ever hope to do is strike an average. 5) In the simulator the load, which is the impedance of the speaker doesn't seem to effect anything but Q, it doesn't effect the frequency cut off. So I don't understand how it will cause spikes in frequency reponse in a class D amp.

Terry
 
#13
TerryG said:



This doesn't make a whole lot of sense to me for the following reasons. 1) I inputed the recomended values of Tripath. 2) The cut off frequency was way above 20K Hz, something like 73K Hz. 3) We all understand the behavior of speakers, what I want to understand is how to figure LC values of the output of a class D amp, and why a Q=0.707? 4) Knowing how speakers have impedance spikes at various frequencies doesn't help, as the best we could ever hope to do is strike an average. 5) In the simulator the load, which is the impedance of the speaker doesn't seem to effect anything but Q, it doesn't effect the frequency cut off. So I don't understand how it will cause spikes in frequency reponse in a class D amp.

Terry
Click to expand...

What Thespeakerguy is saying is that many speakers have an impedance that is rising for higher frequencies, for example most if not all elctrodynamic tweeters (with a voice coil). As a result the the Q-factor of the LRC filter will increase which will result in increased high frequency output. By playing with the LC values, one can influence the response in the high frequency range. A good way could be to linearize the impedance of the speakers at high frequencies by using a zobel network in parallel with the speakers (a series RC network that compensates the rising impedance of the speaker). The zobel network will make sure that the LC filter behaves as desired.

Best regards

Gertjan
 
#14
Oh that makes perfect sense, I was going to get around to asking about why so many Class D amp use a Zobel cap and resistor across the speaker terminals.

For some reason in Evan Shultz calulator it doesn't have a function for this. I think my speakers probably do this more than most, as I have three 16 ohm woofers in parallel and two 16 ohm tweeters, so my impedance is not as low in the upper range. One thing that may help is that my tweeters have L pads on the tweeters, so the amp may see a resistive load on them compared to the woofers. Or would they see a resistive load the more the tweeters are attenuated, and a more inductive load the more they are not?

The zobel network on the Tripath TA2021B chip data sheet has a cap 0.22uf in series with a 10 ohm resistor in parallel with the speaker. So in the upper frequencies the cap is basically making it appear as though the resistor is in parallel with the speaker thus reducing the precieved impedance to the mosfets. This is very useful information because if a person knows their particular speaker and its behavior then they can tune both the output LC and the Zobel.

Terry😎
 
#15
Now that you are talking about zobel networks and LC filter...
This afternoon I was doing some simulations of the feedback of a Class-D amplifier. I was exciting the amp with a square wave, and noticed that there was ringing in the load (varying it from 4 to 40 ohm). After removing all the feedback, itl was still there.
As soon as I have added a Zobel 220nF+10ohm, it has been reduced very noticeably.
About the effect of the Q of the filter: If you reduce the value of the C of the filter to 100nF (I was using 20uH and 440nF), the Q factor is also reduced and the ringing disappears. (of course the carrier rejection is worse).
 
#16
TerryG said:
if a person knows their particular speaker and its behavior then they can tune both the output LC and the Zobel.
Click to expand...


Yes, except for the fact that we don't know the speaker impedance at the switching frequencies - typicaly 650-1000kHz. When was the last ime you say a driver impedance curve plotted that high? 😉

And of course the filter -3dB point is much lower - typicaly 50-70kHz. It would be nice to know the driver impendance at your amp's switching frequency, but how to measure it?

Don't forget that the Zobel is also a protection circuit for the switching MOSFETs when no load is connected.
 
#17
panomaniac said:



Yes, except for the fact that we don't know the speaker impedance at the switching frequencies - typicaly 650-1000kHz. When was the last ime you say a driver impedance curve plotted that high? 😉

And of course the filter -3dB point is much lower - typicaly 50-70kHz. It would be nice to know the driver impendance at your amp's switching frequency, but how to measure it?

Don't forget that the Zobel is also a protection circuit for the switching MOSFETs when no load is connected.
Click to expand...


Why would the speakers impedance curve at those frequencies be relevant? Don't we need the impedance at those frequencies?

Terry😎
 
#18
Pierre said:
Now that you are talking about zobel networks and LC filter...
This afternoon I was doing some simulations of the feedback of a Class-D amplifier. I was exciting the amp with a square wave, and noticed that there was ringing in the load (varying it from 4 to 40 ohm). After removing all the feedback, itl was still there.
As soon as I have added a Zobel 220nF+10ohm, it has been reduced very noticeably.
About the effect of the Q of the filter: If you reduce the value of the C of the filter to 100nF (I was using 20uH and 440nF), the Q factor is also reduced and the ringing disappears. (of course the carrier rejection is worse).
Click to expand...


From what I recently learned the reason for your ringing is because the Q factor on your LC circuit is too high.

Terry😎
 
#19
TerryG said:



Why would the speakers impedance curve at those frequencies be relevant? Don't we need the impedance at those frequencies?

Terry😎
Click to expand...


Terry is correct here, the impedance of the speakers is not very relevant at the switching frequency of the amp as the impedance that the output stage is seeing is largely determined by the L of the LC filter at those high switching frequencies.

For many amps, the zobel is a kind of protection. Some amps need it in cases you use them without load (for example taking the load away during operation). The Q-factor can become sky high and one could get very high voltages at the speaker terminals that maybe killing. For UcD amps, this is not an issue as they take the feedback after the LC filter and compensate for any Q-factor changes by the feedback, as a result, always the same q-factor independent of the load.

Best regards

Gertjan
 
#20
ghemink said:

The Q-factor can become sky high and one could get very high voltages at the speaker terminals that maybe killing.
Click to expand...

Gertjan,

What do you mean by killing? Do you mean the voltages could become dangerous enough to kill someone? Is this because potential is stored in the inductor or capacotor or something that could give you a really bad electrical shock?

Terry
😎
 
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