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Old 24th January 2012, 12:52 PM   #1
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Default Class-D Output Filter - A Case Study

Let me introduce myself since I am new here. I am new to Class-D DIY. I have studied speaker design for about 10 years now, and been a tweaker for over 40 years. I have been designing my own open baffle speaker for three years now and have a fair, but far from thorough, understanding of passive crossovers.

I hope that I can get some input and constructive criticism of what I've written below. I am not as confident of everything as I may sound below.

I recently got a Sure 4x TK2050 board, and have been tweaking it. I found the high frequencies to be too hot in its raw state, and about right with the suggested zobel of 0.47uf and 10ohms.

After much reading and some math, I have concluded that the output filter and zobel of this board is poorly designed and needs to be replaced. Since class-d output filters and zobel must be designed for a specific speaker impedance and voice coil inductance, it is no wonder that class-d reviews are all over the place. But by doing it yourself for you own speakers, I believe you can achieve truly high end results.
By measuring your speaker for the DC resistance (Rs) and voice coil inductance (Ls), you can calculate the output filter and zobel from:

Output Filter:
Cf=1000000*(0.1125/(Rs*f))
Lf=1000*(0.2251*Rs)/f
Cf is the output filter capacitance
Lf is the output filter inductance
f = corner frequency you want for the cutoff
Capacitance comes out in uF, Inductance comes out in mH

Zobel:
For the zobel you can use any online zobel calculator such as:
http://www.carstereo.com/help/Articles.cfm?id=36

After reading the spec sheet for the board and comparing the circuit for the board to the actual board, I found that the board already contains a zobel. On my board it is two tiny orange devices immediately between the speaker output blocks and the output filter. The output of the board is BTL and Sure has split the output filter between the legs as is the usual design. So, for the purpose of studying the output filter we need the single ended version, we must halve the inductance (since the inductors are in series) and double the capacitance (since the capacitors are parallel) to get the actual filter values. Also, the effective speaker impedance is half the actual speaker impedance.
The output filter for the 4x TK2050 from the spec sheet schematic for output #1 is:
L7= 10uH
C5= 0.68uF
Note that this is different than the output filter Sure shows in the spec sheet for the 2x100 board, and these values don't match up with any cutoff frequency I can find in Tripath's literature, the closest being 80,000Hz, L=10uh and C= 0.47uF.
The single ended version of this filter will be:
L= 5uH
C= 1.76uF
All speaker filters are designed for a specific speaker impedance, so we need to know what speaker impedance Sure assumed for their design. But we don't know the Q Sure was shooting for. Most of what I have read says that most manufacturers shoot for a Butterworth Q=0.707. This makes sense to me. So to find the speaker resistance I am going to use the formula from this web site Passive Crossover Slopes and solve for resistance.
Using the output filter inductance we get:
Rs=sqrt((L*Q-squared)/C)=sqrt((5*0.707*.707)/1.76)= 1.19 ohms To get the actual assumed speaker resistance we need to double this, Rspeaker=2.38ohms.
OUCH! This seems way low to me. Most dome tweeters are 4ohms to 8 ohms nominal and resistance rises with frequency due to the driver inductance.
Even if we assume they used Bessel (Q=.58, R=0.98 ohms), Linkwitz (Q=.49, R=0.83 ohms), or Chebychev (Q=1, R=1.69) the results are no better.

I can use equations from another site to calculate the crossover frequency Sure was shooting for, http://www.diyaudioandvideo.com/Calc...Over/Help.aspx, we will assume Sure wanted a Butterworth slope, and these two equations will give us a double check on this, note that L must be in milli-henrys so the value used will be 0.005mH:
Using the inductance:
f=1000*((lratio*R)/L)=1000*((0.2251*1.19)/.005)=53,573Hz
Using Capacitance:
f=1000000*(cratio/(C*R)=53,714Hz
I believe we can say that our assumption that Sure chose Butterworth as their target is correct.
To double check by using values where we know the target, let's take a value from the diyaudio FAQ on modifying the Sure TK2050:
10uH/.47uF = 73,412.76 Hz, single ended values are 5uh and .94uF
If we do the calculations for this we get R=1.63ohms (Rspeak=3.26ohms), and the frequency from inductance 73,382Hz and from capacitance 73,423Hz.

I believe that these double checks show that my calculations of the assumed resistance of the speaker to be correct.

To understand what this means for class-d amps connected to real world speakers lets look at what happens if we connect the Sure to a common tweeter. The Seas 27TDFC, Re=6ohms, Le=0.05mh
The Zobel values then are:
Rz=Re X 1.25 = 7.5ohms
Cz= Le/(Re x Re) = 0.05/(6 x 6) = 0.001389 mF or approx 1.4uF
Sure's Zobel is:
Rz = 10ohms
Cz = .22uf

So, Sure's Zobel is not sufficient and will cause the sound to be too bright in the highs with the Seas 27TDFC.

Also, the Seas tweeter has a 6ohm value and Sure's assumption was that the load would be 3.26ohms. This will cause the filter to peak because the Q of the filter has now increased, adding even more brightness to the sound. Q=sqrt(R*R*C/L)=sqrt(6*6*1.76/5)= 3.6, a huge peak will result.

So, I conclude that the output filter and zobel of this board is poorly designed and should be replaced.
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Old 24th January 2012, 02:19 PM   #2
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Darn, I forgot to include include the BTL version of "designing your own output filter. Here are complete instructions.

By measuring your speaker for the DC resistance (Rs) and voice coil inductance (Ls), you can calculate the output filter and zobel from:

Single Ended Output Filter:
Cse=1000000*(0.1125/(Rs*f))
Lse=1000*(0.2251*Rs)/f
Cse is the SE output filter capacitance
Lse is the SE output filter inductance
f = corner frequency you want for the cutoff
Capacitance comes out in uF, Inductance comes out in mH

BTL Output Filter:
Cbtl=Cse/2
Lbtl = 2*Lse
Cbtl is the BTL output filter capacitance
Lse is the BTL output filter inductance

Zobel:
For the zobel you can use any online zobel calculator such as:
Car Audio - ZOBEL Filters for CROSSOVER Networks
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Old 25th January 2012, 11:47 PM   #3
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Looks about right!
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Old 27th January 2012, 01:11 AM   #4
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If the current inductor on your board looks pretty good, you may be able to keep it and use it in an output filter that exactly matches your speakers. Using the equations, you will be holding the inductor value constant and letting the cutoff freq change. It is the output filter capacitor that will adjust to fit you speakers.

I did a rough approx in Excel and it looks like the freq, often, will not change enough to be a problem. And I am confident that getting the Output filter to match your speakers will make a much greater improvement than changing the cutoff frequency might harm, as long as the frequency stays significantly above 20,000Hz (i.e. 35,000 Hz or so).

To get the capacitor value that will match your speakers, first solve:
f=1000*(0.2251*Rs)/Lf
This gives the new cutoff frequency using the actual value of the on board inductor. Remember to change the value of the inductor from uH to mH for the equation then change it back to uH to get the final value. If the cutoff freq is more than 35,000Hz you can keep the inductor.
Then solve for C:
Cse=1000000*(0.1125/(Rs*f))
This will give you the capacitor for the output filter (not the zobel, don't confuse the two).
You can then unsolder one lead from the on board output filter capacitor (or capacitors if the output is BTL) to disable it. And, Disable the on board zobel by unsoldering one lead on the zobel capacitor or resistor. Now you can add an outboard output capacitor(s) and zobel on the outputs with test leads and play with the values. Don't worry about the stray capacitance and inductance of the test leads. Just keep the leads fairly straight.
If your output is BTL, the capacitors you should use are:
Cbtl=Cse/2
About the zobel:
If you have calculated the appropriate zobel for your speakers using the method mentioned in the first email, you can increase your highs by increasing the zobel resistor, or decrease your highs by decreasing the resistor value. And tweak to your hearts content. :-)
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Old 29th January 2012, 06:13 PM   #5
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I have been playing with the output filter equations and discovered that if you choose 33 uf for the output inductor, and you are willing to let the cutoff frequency change, you could put in a switch and have a separate output capacitor(s) for different speaker resistances, 8 ohm, 6 ohm, and 4 ohm. The cutoff frequency should stay in the acceptable range.
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Old 14th February 2012, 09:22 PM   #6
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hi, thanks for your thread. i wish i was so technical to understand it!
i have a problem with this board. modded it with 4.7uH 0.47uF. 12ohm 0.47uF, to 4ohm speaker. good components.
the sq is much more clear now compare to unmodded. but emphasis on mid and upper mids and the stage is over sized now. is it depend on the Zoble? if i desolder it will the sq go back to the same original neutrality?
it is difficult to test with this board the pads are so tiny. i appreciate any suggestion.
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Old 23rd February 2012, 01:24 PM   #7
Havoc08 is offline Havoc08  Denmark
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I am very interested in this and would like to try different toroid compositions than the crappy Sure ones and maybe go to 68-2 iron powder, but 3F3 or 3F35 look good too. Any input on core material type or is this such a wide topic it warrants a new thread?
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Old 23rd February 2012, 08:46 PM   #8
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Go for a new thread. I am currently using air core inductors I made myself. They sound better than the originals and the upgraded ones.

I made many mistakes in trying to get the right method for matching the output filter to my speakers. Here is the final and CORRECT version. Halving the BTL speaker impedance is included in the equation for BTL output, so use the actual DC impedance value for your tweeter.

Measure the DC Resistance and Voice Coil Inductance of your tweeter (or look it up in the manuf docs).
Then choose one of the standard output inductors and use the following equation to see if the corner frequency of the filter will be acceptable.

fse=1000*(0.2251*Rs)/Lf
fbtl=1000*(0.2251*0.5*Rs)/Lf
Remember to change the value of the inductor from uH to mH before putting it into this equation, then change it back to uH to get the final value. If the cutoff freq is more than 35,000Hz you can keep the inductor, and not too high (I don't know yet what too high is).


Then solve for C:
For Single ended filters:
Cse=1000000*(0.1125/(Rs*fse))
For BTL filters:
Cbtl=1000000*(0.1125/(0.5*Rs*fbtl))
This will give you the capacitor for the output filter (not the zobel, don't confuse the two).

Zobel:
For the zobel you can use any online zobel calculator such as:
Car Audio - ZOBEL Filters for CROSSOVER Networks
Just plug in your tweeter's DC Resistance and Inductance (in mH)

This means that for 4 ohm speakers an inductor value of 15uH or even 10uH (you can keep the inductors on the Sure boards) will work, but 33uH as I suggested in the beginning WILL NOT WORK. 33uH produces too low a cutoff frequency.
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Old 24th February 2012, 03:28 PM   #9
Havoc08 is offline Havoc08  Denmark
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I will.
BTW. Aren't most of the T-amps running BTL or is it only the 12v versions?
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Old 24th February 2012, 04:06 PM   #10
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Quote:
Originally Posted by Havoc08 View Post
I will.
BTW. Aren't most of the T-amps running BTL or is it only the 12v versions?
Most of them are. TA2024, TA2020, TAA4100A and TK2050 are basically always BTL and supplied by a single rail, while TA2022, TA3020 and TK2350 are non-BTL and dual-rail.
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