Question 3.12: Calculate vo (t) for the GG oscillator designed in Example 3......

In the oscillator of Example 3.3 (refer to Figure 3.13): C_{1}=95~\mathrm{pF},~C_{2}=190~\mathrm{pF}, L = 1 μH, R_{S}\,=\,302\Omega,\;R_{D}\,=\,1.25\;\mathrm{k}\Omega, I_{D}\,=\,4.5\,\mathrm{~mA},\,\,g_{m o}\,=6.86\mathrm{~mS}, and g_{m}=4.2~\mathrm{mS}. Therefore, from (3.95),

v_{o}=\left({\frac{\mathbf{C}_{1}  +  \mathbf{C}_{2}}{\mathbf{C}_{1}}}\right)V_{1}\cos\,\omega_{o}t                                  (3.95)

G_{m}=\frac{C_{1}}{C_{1}  +  C_{2}}\frac{1}{\left(R_{s}+\frac{1}{g_{m}}\right)}=\frac{(95  \times  10^{-12})}{95  \times  10^{-12}  +  190  \times  10^{-12}}\,\frac{1}{(302  +  238)}=2.5~\mathrm{mS}

From Figure 3.52, with

{\frac{G_{m}}{G_{m o}}}={\frac{2.5  \times  10^{-3}}{6.86  \times  10^{-3}}}=0.364

it follows that

V_{1}\approx0.7(-V_{P})=0.7(3.5)=2.45\mathrm{V}

Then,

V_{o}=n V_{1}=3(2.45)=7.3{\mathrm{V}}

or

v_{o}(t)=7.3\;\mathrm{cos}\;\omega_{o}t                                        (3.96)

where the frequency of oscillation is 19.75 MHz.
The simulation for this example is shown in Figure 3.13. The output waveform varies between ±7.2V with a fundamental frequency of 19.95 Hz in good agreement with (3.96).