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I have just been reading the Dallas Rangemaster Treble Booster Analysis on:
https://www.electrosmash.com/dallas-rangemaster

It states that the 47uF:

QuoteC3: 47uF electrolytic cap, makes the guitar signal to bypass the R3 resistor. This makes the signal to get higher gain

And adds the formula:

QuoteGv = gm  x Rc =  0.008 x 10K = 80 = 38dB.

note:

gm = 0.008 it was calculated in the Input Impedance section.
38dB is a high voltage gain for a booster pedal, other similar pedals like the MXR MicroAmp have a lower voltage gain of 26dB. This is not necessarily a good or a bad thing, but the Rangemaster will for sure be able to drive signals harder.

But doesn't explain what gm or Rc is of how the uF value of the capacitor feeds into the calculation?

Is it a case of lower value = lover gain, and higher value = higher gain, and by what factor, would you hear a difference using say a small jump to 68uF capacitor, or need to go into the 100's?

> doesn't explain what gm or Rc is

Says "gm = Ie/Vt = 0.2mA/25mV = 0.008"  This is a hasty way of introducing Shockley's Law. Gm of a BJT transistor can be determined just from its emitter current.

Rc is a mis-type. The only 10k resistor in here is called Rv everywhere else.

> how the uF value of the capacitor

"C3: creates a high-pass filter with a fc=1/2πC3xR3 = 1/(2 x π x 47uF x 3.9KΩ) = 0.8Hz (not in the audio band)"

no, a bigger cap doesn't make the gain higher per se. the thing it does is determine at what point the bass is attenuated. you can go as low as 1uf and not really change that much about the sound (especially in font of a cranked amp).
i personally don't recommend electro smash, there are a whole host of mistakes, a lot of them are in formulas, and this can lead to confusion, especially in beginners.

the only way to make the gain higher is change the collector resistor and the bias resistors. although im not sure that the gain can get higher with the particular germanium transistor in the circuit, you might want to change that one too. if you don't mind silicon transistors, i like the sound of a BD139 in a rangemaster-type circuit. (or a 2n3055, it sound good but its a cumbersome size to use in a small pedal.)

cheers, Iain

Thanks, I was trying to get my head around what it was actually doing as I see it used a lot in older boost pedals with a wide variety of values and then sometimes not used at all.

Another way to face it is the intrinsic Emitter resistor (r_e = 1/g_m) which is set in series with transistor Emitter leg..

When Emitter "external" resistor (R3) is bypassed by C3, r_e is still present (125R here) so Q1 gain is set by [RV / (r_e + X_C3)], where X_C3 = 0.159 / C3 x f and f = signal frequency..

You see that, for gain calculated from g_m x RV, you need C3 value to be infinite (X_C3=0) and this only stands for actually (DC) grounded Emitter...

0.8Hz R3/C3 HPF cut-off frequency is the starting point for considering Emitter AC grounded only for R3 >> r_e >> X_C3   so the higher the frequency the lower the X_C3 hence the higher the gain..

P.S.
A slightly more detailed analysis calls for r_e + R3//C3 effective Emitter resistor by which RV should be divided for gain calculation..
(with Collector internal resistance and next stage impedance considered infinite..)

One more question regarding the 47uF caps in the Dallas Rangemaster, I was wondering if these had to be polarized caps or if possible are Non Polar (Bi Polar) caps also suitable to be used in the original circuit?? Thanks

(https://i.postimg.cc/sBv7Snd7/Dallas-Rangemaster-Schematic.png) (https://postimg.cc/sBv7Snd7)

Yes, no problem using bipolar there. No advantage I can think of. But if you got em....

Quote from: carboncomp on November 21, 2020, 12:57:06 PM
Thanks, I was trying to get my head around what it was actually doing as I see it used a lot in older boost pedals with a wide variety of values and then sometimes not used at all.

In such transistor circuits, this cap determines the width of the amplified frequencies. Can vary from 1-100 uf for the audio. Less capacity — less bass. 10-50 uf is enough for the audible range.

Quote from: Dormammu on April 20, 2023, 05:35:39 AM
In such transistor circuits, this cap determines the width of the amplified frequencies.

Strictly speaking, this cap determines each particular frequency amplification.. :icon_wink:

Quote from: antonis on April 20, 2023, 06:42:49 AM

Quote from: Dormammu on April 20, 2023, 05:35:39 AM
In such transistor circuits, this cap determines the width of the amplified frequencies.

Strictly speaking, this cap determines each particular frequency amplification.. :icon_wink:

Nope, the gain is determined by the resistive binding of the transistor. Frequencies above the cutoff frequency of the filter formed by this cap receive the maximum gain possible. As PRR pointed out, anything above 0.8Hz gets a decent boost (for 47uf). By reducing this cap we will reduce the bass boost.
Considering the frequency cut from C1 and C4 (from the bluelagoon picture), there is nothing to even discuss here.
Everything that comes from the guitar through C1 will be boosted to the maximum.

> As PRR pointed out, anything above 0.8Hz

Don't blame me. That's right off the ElectroSmash essay linked in the first message of this thread. (I do agree.)

> In such transistor circuits, this cap

Note that while post #0 asks about "gain" (perhaps meaning frequency response?), that conversation lapsed in Nov 2020, and the person asking has not visited since Nov 2022.

The re-boot "One more question" #5 only asks about polarity, not value or gain/response.

YES, I too think that "old" threads should be grey and dusty so we know if we are re-hashing stale hash.

Quote from: PRR on April 20, 2023, 03:47:59 PM

Don't blame me. That's right off the ElectroSmash essay linked in the first message of this thread. (I do agree.)

Note that while post #0 asks about "gain" (perhaps meaning frequency response?), that conversation lapsed in Nov 2020, and the person asking has not visited since Nov 2022. 

YES, I too think that "old" threads should be grey and dusty so we know if we are re-hashing stale hash.

Oops!! Didn't notice, out of habit the threads with a small number of answers are fresh.   :icon_lol:
I don't blame anyone, I'm just too lazy to give calculations and formulas when there are already those that are next to my thoughts.

Quote from: Dormammu on April 20, 2023, 11:09:57 AM
Nope, the gain is determined by the resistive binding of the transistor. Frequencies above the cutoff frequency of the filter formed by this cap receive the maximum gain possible.

So you presume cap zero impedance above cutoff frequency..

I don't know , Thanks for the replies all in this rehash of an old thread, I believe I have learnt something from all the recent posts, so not to be canned so easily the revitalizing of these old topics, even if the latest question pertaining was a little adrift from the original discussion. All Good, Cheers.  :)

Quote from: antonis on April 20, 2023, 05:18:39 PM

Quote from: Dormammu on April 20, 2023, 11:09:57 AM
Nope, the gain is determined by the resistive binding of the transistor. Frequencies above the cutoff frequency of the filter formed by this cap receive the maximum gain possible.

So you presume cap zero impedance above cutoff frequency..

No, but that's not something to worry about, with C1 and C4 choking basses.  ;)