## Lecture 27 , 28 and 29 :- Oscillators

Common Data : VDD = 1.8V , Lmin  = 0.18µm, µ0N = 350cm2/V s, µ0P  = 100cm2/V s, |VTH | = 0.55, tox = 3.8nm, λ = 0.07V−1, χ = 0.1.

1.Consider a variable delay inverter with delay where is a control voltage to adjust the delay. If this inverter is used to make a three stage ring oscillator, find the oscillation frequency with respect to the control voltage considering 2. Consider a three stage ring oscillator shown in Fig. 41. The varactor capacitance is given by 1. Derive an expression for small signal open loop gain of the circuit in terms of .
2. From the above expression derive the frequency of oscillation. Figure 41 : Figure for Question 2

3. A three stage ring oscillator is made with inverters that have asymmetric delay for the rising and falling edge, due to difference in channel mobilities of and devices .

Given and Will this circuit oscillate. If yes calculate the frequency of oscillation and the duty cycle of the oscillator output .

4. Consider the small signal equivalent of an oscillator as shown in Fig. 42. The inductor has a series resistance of . Estimate the maximum permissible value of in terms of and for sustained oscillations. Figure 42 : Figure for Question 4

5. Consider the oscillator shown in Fig. 43. Capacitance of the varactor is given by   Figure 43 : Figure for Question 5

1. Estimate the gain 2. If a sinusoidal signal overrides over the control voltage, determine the frequency components at the output. Given 6. Consider the oscillator shown in Fig. 44. Treating the transistors to be ideal switches (the output voltage has only fundamental harmonic), sketch the spectrum of the current through the inductor, capacitor and resistor. Figure 44 : Figure for Question 6