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EE121 John Wakerly Lecture #13

Digital-to-analog conversion

Analog-to-digital conversion

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Digital-to-analog conversion

Vout = k (x020 + x02

0 + x020 + … + xn-12

n-1) / 2n

k / 2n = “step size”

reference voltage in “multiplying” DAC

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Weighted resistor networkCMOS

transmission gates

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Norton equivalent

• Equivalent resistance found by setting voltage sources to zero.

• Current source found by setting RLOAD to zero.

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Thevenin equivalent

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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.

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Solution: Ladder Network

• Same Norton and Thevenin equivalents• Uses only two resistor values, R and 2R

– Easy to control resistance ratios on-chip

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Why is it the same?

and so on...

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Analog-to-digital conversion

• Analog comparator = 1-bit A-to-D

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Combinational A-to-D

• Fastest conversion time– used in digital scopes, video sampling, etc.

• Good for only a few bits of resolution

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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

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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; else IDLE with result := result;

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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.

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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.

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Next Time

• Read-only memories (review)• Read-write memories• SRAMs• DRAMs