6.5 A resistor-load inverter with RL = 50 kΩ has the following device parameters:
• VTN(VSB=0) = 1.0 V
• γ = 0.5 V1/2
• tox = 0.05 µm
• µn = 500 cm2/V·s
• W= 10 µm and L= 1.0 µm
A ring oscillator is formed by connecting nine identical inverters in a closed loop. We are interested in finding the resulting oscillation frequency.
(a) Find the delay times of an inverter for an ideal step pulse whose voltage swing is between VOL and V0H i.e., tPHL and tPLH. It should be noted that the loading capacitance of each inverter is strictly due to the drain parasitic capacitance and the gate capacitance of the following stage. For simplicity, neglect the drain parasitics and assume Cload is equal to gate capacitance.
(b) The rise and fall times are defined between 10% and 90% of the full voltage swing. But for simplicity, we will assume that tfall= 2·tPHL and trise=2·tPLH Estimate the actual propagation delays tPHL and tPLH by using the rise and fall times of the inverter and ideal delays found in (a).
(c) Find the oscillation frequency from the information in part(b).
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