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Solutions for Midterm #2 - EECS 145M Spring 2001
1a Successive approximation A/D
D/A Converter
Comparator
Control Logic: Clock, Shift Register, Output Register
Digital Output
Start Conversion
V 1
V (^) ref
V (^) ref
Analog Input
1 b
1 set all bits to zero 2 set index i = N (MSB) 3 set bit i to one 4 send bit pattern to D/A 5 if analog input is less than D/A output, set bit i to zero 6 i = i - 7 return to step 3 (quit if i = zero)
2a Flash A/D
R /
R
R
Address Encoder Logic
Digital Output (N bits)
R /
1
2
2 N โ
2 N โ 2
Exclusive OR
V 1
V ref
V (^) ref
V ref^ โ^ + 0.5โ V
V ref^ โ^ + ( 2 N^ โ 1.5 )โ V = Vref^ +^ โ 0.5โ V
Comparators
2 b
1 Analog input is sent to the (+) inputs of 2 N โ1 comparators
2 (โ) inputs of comparators connected to points between resistors connected in series
3 comparator outputs are sent to a circuit that determines the N -bit address of the highest comparator whose output is one
4 the N -bit address is the converted output
3a
An infinite periodic series of square pulses of width T 0 and period Tr is the convolution of the
square wave h ( t ) with an infinite periodic series of delta functions:
g t t kTr k
=โโ
โ
By the Fourier convolution theorem, the Fourier transform of h ( t ) convolved with g ( t ) is the simple product of the individual Fourier transforms H ( f ) and G ( f ):
G f H f
T f T f
f (^) r f nf (^) r f T n
( ) ( ) (^) r r
sin( ) = ( โ ) = / =โโ
โ
ฯ ฯ
(^0) ฮด 0
This Fourier transform has the envelope of H ( f ) but is non-zero only at integer multiples of the repeat frequency fr.
3b For T 0 = 1 ฮผs and T (^) r = 1 ms
f (kHz)
-1^3
The Fourier transform is non-zero only at integer multiples of the repeat frequency fr = 1 kHz
Midterm #2 class statistics:
Problem max average rms 1 20 15.1 5. 2 20 15.3 5. 3 20 14.4 5. 4 40 26.8 6. total 100 71.5 14.
Grade distribution:
Range number approximate letter grade 46-50 2 Cโ 51-55 0 56-60 2 C+ 61-65 1 Bโ 66-70 2 B 71-75 2 B+ 76-80 1 Aโ 81-85 2 A 86-90 2 A 91-95 1 A+ 96-100 0
6 Aโs; 5 Bโs; 4 Cโs
