Solutions to ECE 4420 - Spring 2005 Homework 1: Delay Calculations in Electronic Circuits, Assignments of Electrical and Electronics Engineering

Download Solutions to ECE 4420 - Spring 2005 Homework 1: Delay Calculations in Electronic Circuits and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! ECE 4420 – Spring 2005 Page 1 Homework 1 – Solutions Problem 1 This question is as easy as it looks, no tricks here. a. The delay from ‘a’ to ‘b’ is simply the delay of an inverter times the number of inverters which would be 10 ns. b. i. The period in this case is simply twice the delay around the loop, T=20 ns. ii. The frequency is 1/T =50 MHz. Problem 2 The delay of an RC circuit with a step input applied is: ( ) 1.2(1 )t RCV t e−= − In our case, we are solving for t: a.) For V(t)=0.6V: ( )3 15 101.212.5(10 ) (100)10 ln 12.5 10 ln 2 866 s 0.6 t p− − = × = =    b.) 1.2V: t = ∞ This circuit will never read 1.2V. c.) The delay from 10% to 90% VDD: 10% 0.1 (1 ) 132 t RCe t ps − = − ∴ = 90% 0.9 (1 ) 2.88 t RCe t ns − = − ∴ = 90% 10% 2.88 0.132 2.75 st t t n= − = − = ECE 4420 – Spring 2005 Page 2 Problem 3 The delay for 0 and 0 uses the exponential rise/fall equation: a.) For RDOWN: ( ) 1.2 8.66t RC DOWNV t e t ms − = ∴ = b.) For RUP: ( ) 1.2(1 ) 20.8t RC UPV t e t ms − = − ∴ = c.) The ratio of delays is: 20.8 2.4 8.7 UP RATIO DOWN tt t = = = or 0.42 (depending on which way you did the ratio.) Problem 4 a) The solution for the NMOS case is based on Example 2.4: The equation for VT0 is: 0 2 BT FB F OX QV V C φ= − − Calculate each individual component. 17 10 ( ) 13 6 2 OX 0 7 7 2 0 0 6 11 19 6 3 10ln 0.026ln 0.44 V 1.4 10 0.44 0.55 0.99 V 4 3.5 10 F/cm 1.6 10 F/cm 3 103 10 / 0.188 V 1.6 10 6 10 1.6 10 0. 1.6 10 i Fp A GC Fp G gate OX B B OX OX OX nkT q N C QQ C cm C Q C φ φ φ φ ε ε − − − − − − − × = = − = − × = − = − − = − = = × = × × = × = = × × × × = = × TO 06 V V 0.99 ( 0.88) ( 0.188) 0.060 0.018 V= − − − − − − = +