### Author Topic: Rangemaster's 47uF cap and it relation to gain?  (Read 475 times)

#### carboncomp

##### Rangemaster's 47uF cap and it relation to gain?
« on: November 20, 2020, 09:04:41 PM »

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

It states that the 47uF:
Quote
C3: 47uF electrolytic cap, makes the guitar signal to bypass the R3 resistor. This makes the signal to get higher gain

Quote
Gv = 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?

#### PRR

##### Re: Rangemaster's 47uF cap and it relation to gain?
« Reply #1 on: November 20, 2020, 11:18:49 PM »
> 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)"
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#### iainpunk

##### Re: Rangemaster's 47uF cap and it relation to gain?
« Reply #2 on: November 21, 2020, 10:47:56 AM »
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
« Last Edit: November 21, 2020, 10:54:30 AM by iainpunk »
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#### carboncomp

##### Re: Rangemaster's 47uF cap and it relation to gain?
« Reply #3 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.

#### antonis

##### Re: Rangemaster's 47uF cap and it relation to gain?
« Reply #4 on: November 21, 2020, 02:04:54 PM »
Another way to face it is the intrinsic Emitter resistor (re = 1/gm) which is set in series with transistor Emitter leg..

When Emitter "external" resistor (R3) is bypassed by C3, re is still present (125R here) so Q1 gain is set by [RV / (re + XC3)], where XC3 = 0.159 / C3 x f and f = signal frequency..

You see that, for gain calculated from gm x RV, you need C3 value to be infinite (XC3=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 >> re >> XC3   so the higher the frequency the lower the XC3 hence the higher the gain..

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