Page 213 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

+ Vout

NL
VBE
Res R1 L1 C1

FIGURE 13-98 Alternative diagram for a Colpitts oscillator.
For the values given where RI = 2,700

, RE = 1,000 V, Cl = 0.0018 ~F, C2 = 0.056 ~F, and Ll = 15 ~H, the resonant
frequency is about 1 MHz, thus providing a 1-MHz signal' at the emitter or collector

of Q1. With 1.7 volts at the base of Ql, the emitter DC voltage is about 1 volt,
which sets up a collector current of 1 mA. The current gain ~ is greater than 10
(e.g., typically 100 or more). The 1-mA collector current provides a small-signal
transconductance gm of 0.038 mho (amperes per volt).

Since at 1 ,MHz C2's impedance almost grounds the emitter or Ql, the initiall gain of
the system is (gmRL)(l/ n), where 1/ n is the step-down ratio Cl/(Cl 1 C2) = 1/31
for this example. Therefore, the initial gain of the system Av = 0.038 x 2,700/31 =
3.2. Normally, the initial small-signal gain of this type of oscillator is between 2.2
and 4. A higher initial small-signal gain can be set, but at the expense of generating

more distortion with a larger-amplitude output voltage.
From the initial small-signal gain of Av = 3.2, a reasonable prediction can be made
as to what the input amplitude will be. It turns out that l/Av = 1/3.2 = 0.312 is also

approximately Gm/gm that is, in other words,

/

From Table 13-2, when Gm/gm = 0.304, the input voltage is about 156 mV. So we

can expect with Gm/gm = 0.312 that the input signal voltage across C2 will be on
the order of about 156 mV.