1. EE121 John Wakerly Lecture #13
Digital-to-analog conversion
Analog-to-digital conversion

2. Digital-to-analog conversion
Vout = k (x020 + x020 + x020 + … + xn-12n-1) / 2n
reference voltage in “multiplying” DAC
k / 2n = “step size”

3. Weighted resistor network
CMOS transmission gates

4. Norton equivalent
Equivalent resistance found by setting voltage sources to zero.
Current source found by setting RLOAD to zero.

5. Thevenin equivalent

6. Weighted-resistor network problems
Resistor values span a wide range
n-bit DAC ==> resistors from 2R to 2nR
8-bit DAC ==> 2R to 512R, e.g., 2K to 512K
Difficult to fabricate wide ranges of resistance in semiconductor processes.
Different resistors in the network have different accuracy requirements.
5% resistance change at MSB has 2.5% effect
5% resistance change at LSB (8-bit) has .02% effect
MSB of 16-bit DAC (as in CD player) would require accuracy of one part in 215 (.003%) to have less than one step-size error.

7. Solution: Ladder Network
Same Norton and Thevenin equivalents
Uses only two resistor values, R and 2R
Easy to control resistance ratios on-chip

8. Why is it the same?
and so on...

9. Analog-to-digital conversion
Analog comparator = 1-bit A-to-D

10. Combinational A-to-D Fastest conversion time
used in digital scopes, video sampling, etc.
Good for only a few bits of resolution

11. Sequential A-to-D
Idea: Use one comparator, repetitively, and a DAC to try different digital values until correct result is found.
“COMP”
(logic signal)
RESULT

12. Counter-ramp A-to-D Initialize result register to 0
Keep incrementing result register until the DAC produces a votage greater than Vin.
Maximum of 2n steps for n-bit conversion.
ABEL code:
state IDLE: if START then LOOK with result := 0;
else IDLE with result := result;
state LOOK:
if (COMP == 1) then DONE with result := result;
else if (result == MAX) then DONE with result := result;
else LOOK with result := result + 1;
state DONE: if START then DONE with result := result;

13. Successive-approximation A-to-D
Like a binary search in software -- n steps to search 2n possible results (n-bit result).
First step -- determine MSB of result:
Set result to 100…00. Is COMP 1 or 0?
COMP=1 ==> MSB = 1; else MSB = 0.
Second step -- determine next lower bit:
Set result to x10…00. Is COMP 1 or 0? (x = bit found at previous step).
COMP=1 ==> next lower bit =1; else 0.
And so on, for n steps through the LSB
Lab assignment -- create state machine and result register for this algorithm in ABEL.

14. Apple ][ A-to-D converter
Converts analog position into numeric value.
Idea:
Use a potentiometer whose resistance is a function of position (e.g., on a joystick).
Combine the resistance with a capacitance and measure the RC time constant use a program loop.

16. Next Time
Read-only memories (review)
Read-write memories
SRAMs
DRAMs