RangeFinder Boost (Rangemaster) – Frequency Response

[benny_profane]

Here's a list of the corner frequencies for the selectable caps with the RangeFinder project. This uses the equation fc=1/(2πC1xZin) and assumes an input impedance of 12KΩ.

• 2n2: 6.0KHz
• 4n7: 2.8KHz (stock rangemaster)
• 6n8: 2.0KHz
• 10n: 1.3KHz
• 22n: 600Hz
• 47n: 280Hz
• 100n: 130Hz
• 1µF: 13Hz (full frequency)

 

[Chuck D. Bones]

How did you get 12KΩ? It's certainly in the ballpark, but will vary with the BIAS setting and hfe.

 

[benny_profane]

How did you get 12KΩ? It's certainly in the ballpark, but will vary with the BIAS setting and hfe.

That value is certainly going to be variable depending on Ge device’s hFE and particular bias. I used the values from electrosmash because it used the stock biasing resistors. The hFE they use is a little high (i.e., 100), but it’s an even number. The Fc chart was intended as a reference (reflected in the generous rounding) and not absolute values.

If folks want exact figures, here’s the calculation for Zin:

Zin = (R1//R2) // (Zin transistor)

Note: ‘//’ represents resistors in parallel; calculate values using equation for parallel resistors.

Do not use a DMM or transistor tester (save for a peak atlas unit that accounts for leakage) to determine gain of a Ge transistor; you will NOT get an accurate reading. The leakage will be added to hFE value and give a misleading reading or—without knowing the exact test circuit architecture—the figure will be almost entirely meaningless. Si devices can be tested with these methods no problem. Reference this article to obtain reliable hFE and leakage figures for Ge transistors:

http://www.geofex.com/article_folders/ffselect.htm

Detailed calculations for input impedance:

rπ = [(β+1)xVt]/Ieq = β/gm = 100/0.008 = 12.5KΩ

β = 100, default Ge hFE; replace with your device’s hFE value.

gm = Ie/Vt = 0.2mA/25mV = 0.008

Ie= 0.2mA (see equations below)


Calculating the Base voltage:

Vb = Vcc x R1/(R1+R2)/= 9 x (470KΩ/(470KΩ+ 68KΩ)) = 7.8V (8V approx.)
The Base voltage (defined by R1 and R2) will determine the Base current:

Vb = Vbe + (β+1) x Ib x R3

ib = (Vb - Vbe) / (R3 x (β+1))

ib = (7.8 - 0.3) / (3.9KΩ * (100+1))

ib = 0.0195mA

Note:

• Vbe=0.3V for most of Germanium transistors.
• We are using a default value of transistor Hfe = β = 100

The collector current and Collector Voltage will be:

Ic = β x ib = 100 x 0.0190= 1.9mA (2mA approx)

Vc= -Ib x Rv = -0.2mA x 10KΩ = -2V.

It is important to understand, that following the equation, if the β value changes, the bias point will change too. This is why using a trimmer resistor instead of R2 will compensate for this β variation.

Further reading:

ElectroSmash - Dallas Rangemaster Treble Booster Circuit Analysis

Electronic analysis of the Dallas Rangemaster Treble Booster circuit.

www.electrosmash.com

 

[Chuck D. Bones]

Wow, nice work! Very detailed. To put some bounds on it, we won't dial in Ic any greater than about 0.5mA or much less than 0.1mA. Beta (hfe) will range from maybe 50 - 100, mostly landing closer to 60 - 70. Sure you can get higher beta germaniums, but they're wasted on a RangeMaster. So rπ will range from 2.5K to 25K.

The other thing that figures into RangeMaster frequency response is pickup impedance...