Boucherot cell (Zobel network) values
Generally the resistor value choosen for the Boucherot cell seems to be 2.7R here at diyaudio.com. Why is that? Wikipedia claims that the values often is in the range of 5R to 10R.
Is there anyway to calculate this value? I guess there is but how important is it? Would a 2.5R do the job as well as 2.7R?
If the amplifier document mentions the name Boucherot Cell, then I'd have to guess you're making a TDA7294 based amplifier? From practical application, those seem to appreciate 4 ohms or larger values because that chip will automatically step down the output power in presence of a stronger load.
There is a great debate about the resistor value. The value of 2.7R was published in National Semiconductor documents for their Overture amplifiers.
Some believe that the value is a mistake, some believe its audibly harmful to sonics, but I beleve that the intention was for large scale production to use an extremely economical polyester capacitor's typical very high ESR (internal resistance) in addition to that 2.7 ohm resistor.
There is, however, no guarantees on satisfactory audio results with 2.7 ohm resistors in amplifier speaker output zobels.
That's because the average ESR approach doesn't indicate any reliable figure during a specific bandwidth (like your upper treble that may get brutalized because the appropriate amount of additional resistance did not occur at that specific bandwidth), so however you look at it, 2.7R (and smaller values) could be a blunder.
One sure-fire solution is to measure the DCR (reference load) of your current speakers. For instance, 8 ohm speakers probably resist DC at 6 ohms. You can use that as a resistor value along with polypropylene (MKP) capacitors that are currently in style. Thus, the wikipedia value of 5 ohms is very close to generally good. ;)
Capacitor values include 0.22uF, 0.1uF, and 0.047uF. Given that one wishes to avoid impact on the audio band, I believe that the decision on the capacitor value can be done by ear (an excellent detector in the audio band).
Bridged amplifiers need special treatment. This needs two zobels, and each at "half strength," twice the resistor value with half the capacitor value--when two amplifiers are bridged, according to ST Thompson. Maybe I errored in the description? Anyway, the sum total of the two should be the same value as a normal single zobel. I have no documentation for parallel amplifiers.
The technical reason for this network is to frequency compensate the output stage and even more in combination with a capacitive load. The values are not particulary sensitive but the main thing is to let the output have a resistive load of some decent value and 2.7 - 10 ohms seems reasonable. 2.5 ohms may also be OK. have you read the application note An-1192?
Thank you for your answers.
Danielwritesbac: No it's not a TDA-based amp. It's a LM3886-based board with 3 LM3886 in parallel. PA150-config with DC-servo, see attached image. Boards are ordered and I attend to use them in a bridged/parallel configuration. The main reason why I asked is that I discovered that the resistors I wanted to use dont come in the value of 2.7R. Then I started thinking about why that value seems to be the generall choosen one in all configuration I have seen here, since I have read different suggestions at Wikipedia for example.
Your detailed answer has answer my thoughts. People here dont really know why they put 2.7R, they just do it because everyone else do it ;)
Peranders: Yes I have read AN-1192. National only mention this under the partlist for the PA100-schematic, as a "Snubber Network on Output" on page 16. I cant find any other detailed information about it. It's also in the Overture Design Guide but no detailed axplenation about it in there to.
This, I confirmed; however. . . for LM3886, it will not affect the power output, but could turn the resistor brown (LM1875 certainly does) or make the already loud midrange "seem" even more intense because a too-strong zobel could limit the upper treble (applies to LM3886). Perhaps your BP application has a nicer, more open, frequency density than a solo chip. I'd sure like to know.
The resistors you wanted? The zobel component will be most useful if its resistor is sturdy and metal, so that it may reach to and shunt away RF. Just remember that this is a non-audio shunting component, which, being a zobel, is a masking component as well. Its just that the part you "want" is likely to have the opposite effect on sound if used in a shunt role.
I think you just need 1 watt minimum capacity and metal; however, its brand and visual styling won't matter.
As for the rest, and as for the exact figures, I'm stepping out of the way before I step into. . . something unoptimized. ;)
This output RC does several things:
1) together with the open-loop Rout of the amplifier it forms a pole and a zero in the open-loop gain, which, if choosen properly, reduce risk of feedback loop instability with capacitive load. Wrong values increase instability, though.
2) it compensates/damps oscillation tendencies of capacitively loaded emitter followers.
3) with quasi-comp. outputs (the bottom of the LM3886 etc is a NPN-Power transistor in a CFP hookup) it damps the tendency of oscillation of the CFP output.
2) and 3) are the more important parasitic effects, 1) is a control loop theory thing which is more or less insignificant when the snubber R >> Rout (that is, the pole and the zero are too close), which is quite often the case. Therefore the best values are normally found empirically.
4) It can be "misused" to linearize/flatten the speaker impedance at HF. This should better be done after a series L//R and right at the speaker (where it could be dimensioned to approach cable HF impedance to terminate it, which is of importance with high bandwidth amp -- not chip-amp territory, typically)
The cap isolates DC/LF current and is normally choosen to kick in just above the audio range (but still it must be capacitive at HF, which is actually more important), while the resistor is the part that "does the work", and it must be a low inductance type and also wired with low inductance, btw preferably directly to the neg. supply (which must be bypassed also directly to the pos. supply, or alternatively split up the snubber cap in a center tapped cap between the supplies).
Thanks KSTR for that.
I would like to add that the output Zobel attenuates interference and back EMF that tries to enter the inverting input of the amplifier.
If the Zobel is part of the full Thiele network then the attenuation is much better.
According to Philips (Mullard) in their book Transistor Audio and Radio Circuits (1969) the purpose of a Zobel (Bucherot) network is to modify the load on an amplifier so that it appears totally resistive. So reducing any voltage spikes and current spikes on the output transistors.
A Zobel network is a capacitor Cz and a resistor Rz in series placed in parallel with the load of an amplifier.
The values of Cz & Rz are calculated as follows.
If the Loudspeaker is considered equivalent to a series resistance Rs in series with an inductance Ls then:
Rz = Rs
and Cz = Ls/(Rs*Rs)
When these conditions are satisfied then the parallel connection of the Zobel network and the Loudspeaker will present a purely
resistive load to the amplifier. In practice this is of course only an approximation as no correction is made for stray capacitance or lead impedances and a loudspeaker is not exactly an inductance in series with a resistor but the analogy is sufficient to reduce the loading on the output transistors.
The values of Ls and Rs can be found from the Thiele-Small parameters of the loudspeaker.
The Mullard book also claimed better breakdown performance as the amp sees a more resistive load.
KSTR's point 3 The bottom half of the quasi output has a PNP inverter which in the early days of monolithic amps had a lousy frequency response and the amp would go unstable, so the output RC was a convenient way to slug the high frequency response and provide stability. The higher the resistor can be and the lower the capacitor is a sign that the amp has a good PNP response. For discrete amps with better PNPs the RC is typically 10ohm and 0.1uF
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