Analysis of power amplifier bias circuit: does it need to be thermally bonded?

Question

I'm in the process of building a medium power amplifier for the 20m band (14MHz) and I'm experimenting with bias circuits. The amplifier is a classic BJT push-pull arrangement with a transformer input having a centre tapped secondary into which the bias is fed.

I've come across the bias circuit shown below and I've been using it with mixed results.

^{simulate this circuit – Schematic created using CircuitLab}

One thing I haven't done is thermally bonded the controlling transistor (Q2 above) to the power transistor heatsink (I should clarify that this is the heatsink for the push-pull power transistors and not Q1 shown above) and I wanted to generate an expression that would indicate how the output (Vout) changes with the temperature of Q2. I always find these coupled transistor circuits difficult to analyze, but I've arrived at an expression for VE that I find interesting.

$$V_{b1}=V_{cc} - I_c R_c$$

$$V_{E} = V_{b1} - V_{be1} = V_{cc} - I_c R_c - V_{be1}$$

$$I_{c} = I_{b2}\beta_2$$

$$I_{b2} = (V_{E} - V_{be2})/R_{b} - V_{be2}/R_{\text{adj}}$$

If I combine these expressions into an equation for VE, I get:

$$V_E = \frac{V_{cc}+V_{be2}(\beta_2 R_c R_t)-V_{be1}}{\beta_2 R_c R_{\text{adj}} + 1}$$ where \$R_t = R_b + R_{\text{adj}}\$

If we assume the Rt is equal to Radj and neglect the + 1 in the denominator, then as Q2's beta rises due to temperature, the value of VE would seem to drive towards Vbe2. Do I have that right?

But, Vbe2 is decreasing as a result of the rise in temperature. Does this suggest that Q2 should be thermally bonded?

Answer 1

Don't depend on beta changing with temperature; it's too unpredictable. Best to assume beta is infinite initially and then analyze the effects of (negligible) base current.

If VE is considered an output, its value is VBE(Q2)*(RADJ+RB)/RADJ. If you want this to track some other circuits, then Q2 needs to be thermally coupled to them. Q1 is not particularly critical in the circuit.

Base current of Q2 (approximately VC/RC/beta) might be about 13.7/820/50 = 300 uA. 300 uA in RB (100 Ω) is 30 mV -- this variation is negligible in your circuit.