Let's shake hands for Beta = (Base voltage / Collector voltage) X (Base resistor / Collector resistor)..

Beta = Collector Current / Base Current

Collector Current = Collector Voltage / Collector Resistor

but

Base Current = (Supply Voltage - Transistor Base Emitter Voltage) / Base Resistor

So when you write an equation with the same form as those posted you get,

Beta = (Collector Voltage / Collector Resistor) * (Base Resistor / (Supply Voltage - Transistor Base Emitter Voltage))

Beta = (Collector Voltage / (Supply Voltage - Transistor Base Emitter Voltage)) * (Base Resistor / Collector Resistor)

The difference is the denominator of the first term "Base Voltage" vs "Supply Voltage - Transistor Base Emitter Voltage"

Picking transistors for FF Clones

http://www.geofex.com/Article_Folders/fuzzface/fftech.htmThe way I look at the circuit is to start with a ball-park collector current. A good test current is 1mA to 2mA, as that's what is often used in datasheets. A ball-park middle transistor gain is beta = 300, so the ball-park base current is 5uA.

After that I don't try to write out a whole equation. Go a step at a time. That lets you keep your hands

on the wheel about what is going on.

1) Work out what resistor is required for a base current around 5uA.

*** The whole basis of the circuit is to operate at a constant base current. ***

Base Resistor = (Supply Voltage - Transistor Base Emitter Voltage) / Base Current

= (9 - 0.65) / 5e-6

= 1.67M

VBE of 0.65V isn't a bad estimate for 1mA to 2mA collector current. At a squeeze you could argue for 0.62V.

The accuracy of the circuit just isn't there for splitting hairs and different transistors will have different

VBE's even at 1mA. The circuit doesn't keep the collector at a constant current anyway and that causes

VBE to move with different hFE (assuming the same transistor type).

RG's choice of 2M2 is perfectly acceptable.

2) Once the base resistor is chosen we can work out the actual base current,

Base Current = (Supply Voltage - Transistor Base Emitter Voltage) / Base Resistor

= (9 - 0.65) / 2.2M

= 3.7955uA

3) We want hFE = 100 * collector voltage.

For hFE = 300 we need 3V out. We just need to pick a point so we have some concrete numbers.

With the base current in (2) the collector current is,

Collector Current = 300 * 3.7955uA = 1.1386mA

4) Now we choose the collector resistor to have 3V drop with this collector current.

Collector Resistor = 3 / 1.1386mA = 2634.7 ohm

[If you want to be precise, that's the require final value including the multimeter loading.

For a 1M ohm input impedance multimeter, the actual resistor value is Rc = 1/(1/2634.7 - 1/1M) = 2341.7 ohm

For a 10M ohm input impedance multimeter, the actual resistor value is Rc = 1/(1/2634.7 - 1/10M) = 2635.4 ohm

Don't forget tolerances on the 2M2

]

5) If the collector voltage rises much above 8V the transistor's VCE will be too low to guarantee

the transistor isn't saturating. Since hFE = 100 * collector voltage = 100 * 8V = 800.

The circuit will measure a maximum hFE of 800.