Last month, the first half of this article introduced the large-signal approach to oscillator design. This concluding section will offer some VHF/ UHF design examples, including the 144-MHz oscillator first presented last month in Part 1.

The component values for the 144-MHz oscillator (C₁, C₂, C₃, C₄, and L) can be calculated in the following way. First, the values of capacitors C₁ and C₂ can be found from the following approach. The value of capacitor C₁ is selected for proper loading according to Eq. 32 (see box 1 for equation).

If using a ratio of C₁/C₂ = 4, then the value of capacitor C₂ is approximately 11 pF.

The values for capacitors C₃ and C₄ can be found by again choosing for optimum phase noise and output power, in which case:

and the capacitive transformer tapping ratio m (C₃/C₄) should be greater than 10; therefore, the impedance transformation is greater than 100. Thus, for a value of C₃ of 22 pF, the value of C₄ is 220 pF. Again one needs to use as many as 10 parallel capacitors or a very low-parasitic one that is capacitive to more then 1 GHz.

4. The value of inductor L can be calculated from Eq. 34 (see box 1 for equation). For f₀ = 144 MHz, the value of the inductance L₃ can be found from Eq. 35 (see box 1 for equation).

The L/C ratio for the 144-MHz oscillator can be calculated in the following way. The energy stored across the resonator circuit for a given conduction angle and drive level is dependent on the characteristic impedance, and can be found from Eq. 36 (see box 1 for equation).

For optimum phase noise and output power, Z should be greater than 3. For example, the L/C ratio for a good approach is

The same test circuit for the small-signal analysis can now be used with the new large-signal component values applied. Reference 9 shows the phase-noise calculations for a Colpitts oscillator. The calculations can also be used to find the phase noise for the 144-MHz oscillator circuit. Using the Nexxim HB simulator from Ansoft Designer, the simulated phase noise agrees closely with measured data.

According to ref. 9, the individual phase noise contribution can be described by using Eq. 38 (see box 1 for equation), as well as Eqs. 39-42 (see box 2 for equations). The total effect of all the four noise sources can be expressed as the function shown in Eq. 43 (see box 3 for equation).
where
K_f = the flicker noise constant,
AF = the flicker noise exponent, and

It should be noted that the effect of the loading of the Q of the resonator is calculated by the noise transfer function multiplied with the sum of the four noise sources.

The next step for the 144-MHz oscillator is to compute the phase-noise contribution from the different noise sources for the parallel tuned Colpitts oscillator circuit at a frequency offset of 10 kHz from the oscillator carrier frequency (f₀) of 144 MHz. This is performed by considering the circuit parameters. For example, the base resistance (r_b of the transistor is 6.14 ohms while the parallel loss resistance of the resonator (R_P is 7056 ohms. The Q of the resonator (the Q of the inductor at 144 MHz) is 200, the inductance of the resonator is 39 nH, and the capacitance of the resonator is 22 pF. The transistor collector current (I_c) is 10 mA while the base current of the transistor (I_b) is 85 µA. The device flicker noise component (AF) is 2 while the flicker noise constant (K_f) is 1 ×10^-7. The feedback factor (n) is 5. The phase noise at an offset frequency of 10 kHz for the four noise sources can be found by applying Eqs. 45, 46, 47, and 48 (see the box 4 for equations).

The sum of the four noise sources can be expressed as expressed in the relationship shown as Eq. 49 (shown in box 5).

Continued on page 2