Collector-Base capacitance in simple FM transmitter

Question

Here is a schematic of a simple FM transmitter. I understand that this work in the following way: the sound picked up by the mic is translated into a voltage at the base of the Q1 transistor. As the internal base-collector capacitance of a BJT depends on the base-collector voltage, the B-C capacitance changes with the sound signal. This internal capacitance forms a resonant circuit with C1, C3 and L1. The resonant frequency of this circuit changes as B-C capacitance changes, and so the signal is FM modulated with the sound signal.

But how do I work out the frequency of the FM signal by reading this schematic? Let's say there is no sound signal. I set VC1 to a known capacitance. I know that C1 is large enough so it offers no impedance for the FM signal and therefore the base is effectively grounded for the FM signal. C3 is even bigger. So therefore we have, in effect, L1 directly parallel with VC1 and B-C capacitance. To get the total capacitance in parallel with L1, I need to add VC1 and B-C capacitance.

But how do I know the capacitance of the B-C junction? Let's say I want to know the base frequency (no sound signal), how much capacitance is there? I don't see C-B capacitance as a function of C-B voltage on datasheets.

Answer 1

In this circuit, collector-to-base capacitance would be close to \$C_{ob} \$. The base is almost grounded by C1 as far as radio frequency is concerned.
\$ C_{ob} \$ is typically 2.5pf, maximum of 4pf when the DC collector-to-base voltage is 5V.(From a National Semiconductor data sheet). This measurement was done at 1MHz, not at 100MHz where this circuit is usually meant to operate. From the 2N3904 data sheet by ON semiconductor, \$C_{obo} \$ corresponds to collector-to-base capacitance:

This graph will not be useful if you wish to include \$ C_{ob} \$ in calculation of oscillation frequency, since \$C_{ob} \$ has a relatively minor affect on frequency, compared to other capacitances. Not shown on the schematic are stray capacitances and inductances, and the reactive component added by the antenna. Besides strays, the inductor's self-resonant frequency is likely unknown. Tolerance of small-value inductor and capacitors is often poor, and their values are modified by inductance of connecting wires.
At 100MHz, the 2N3904 hasn't much gain, and is likely running close to its gain*bandwidth limit: a carefully-done internal model would be required.
As others have said: you build it and verify that it oscillates by searching for its frequency with measurement tools. Then you vary component values in an attempt to move frequency up or down. (VC1 variable capacitor is meant to modify frequency, but 100pf seems somewhat too large). This is by no means a stable and predictable oscillator at 100 MHz.