Question 3.9: Design the Clapp oscillator in Figure 3.30a to oscillate at ......
Design the Clapp oscillator in Figure 3.30a to oscillate at 10 MHz.
The BFS17P BJT was selected for this design. This RF transistor lists a maximum f_{T} value of 2.5 GHz. At a typical Q point of V_{C E}=5V\mathrm{and}\;I_{C}=2\;\mathrm{mA}, the value of f_{T} is 1.5 GHz.
The Q point is obtained with V_{\mathrm{CC}}=10\mathrm{V},\;R_{E}=2.5\;\mathrm{k\Omega},\;R_{1}=4.3\;\mathrm{k\Omega} and R_{2}=5.7\ k\Omega. The value of g_{m}\, at I_{C} = 2 mA is 80 mS.
Let L = 25 μH with {Q}_U = 80. Then, X_{L}=1,571\Omega at 10 MHz and
R_{s}=\frac{\omega L}{Q_{U}}=\frac{2\,\pi \times 10^{7}(25 \times 10^{-6})}{80}=19.6\Omega
From (3.67), with C_{1}=C_{2}, we obtain
\frac{g_{m}}{\omega_{o}^{2}\,C_{1}\,C_{2}\,R_{s}}\gt 1 (3.67)
C_{1}^{2}\lt {\frac{g_{m}}{\omega_{o}^{2}R_{s}}}={\frac{0.08}{(2\pi \times 10^{7})^{2}19.6}}=1.04\times10^{-18}
or C_{1}\ll1 nF, which is satisfied with C_{1}=C_{2}=100 = 100 pF (or X_{C_{1}}=-159\Omega).
The value of {{C}}_{3} follows from
X_{C_{3}}=-X_{L}-X_{C_{1}}-X_{C_{7}}=-1,571+159+159=-1,253\Omega
or {C}_{3}=12.7{\mathrm{~pF}}. The total capacitance across L is \mathbf{C}_{T} = 10 pF.
The simulation of the oscillator is shown in Figure 3.31. The fundamental frequency of oscillation is 10.01 MHz.
