Digital to Analog Conversion using Resistors

This is the most simple way of converting digital signals into an analog voltage. The circuit is shown in figure 1. The values of the resistors are 2^(m-n) multiples of the resistor value of the most significant bit (MSB). In out example m=4, R(D4)=1k
R(D3)=1k * 2^(4-3) = 2k
R(D2)=1k * 2^(4-2) = 4k
R(D1)=1k * 2^(4-1) = 8k
R(D0)=1k * 2^(4-0) = 16k

Fig. 1: Simple resistor digital to analog converter

To test the circuit the input D0 to D4 are stimulated using pulse sources. The corresponding SPICE netlist is shown below:

*SPICE circuit <RDTA> from XCircuit v3.30

R1 D0 AOUT 16k
R2 D1 AOUT 8k
R3 D2 AOUT 4k
R4 D3 AOUT 2k
R5 D4 AOUT 1k

* stimulus added manually creating a ramp
V0 D0 0 pulse 0 1 1n 1n 1n 9n 20n
V1 D1 0 pulse 0 1 1n 1n 1n 19n 40n
V2 D2 0 pulse 0 1 1n 1n 1n 39n 80n
V3 D3 0 pulse 0 1 1n 1n 1n 79n 160n
V4 D4 0 pulse 0 1 1n 1n 1n 159n 320n
* a little capacitive load eases convergence
C1 AOUT 0 0.1p
.end

(If you want to play with SPICE here is the netlist itself: RDTA.in )
The simulation shows a decreasing quantisized ramp

Limitations of the design

The circuit has two drawbacks hindering integration:
1. The circuit requires a very wide span of resistor values. A 10 bit DTA would lead to a ratio of 1024 between the resistor of bit D9 and the resistor of bit D0. This is extremely expensive to integrate.
2. The resistors of the most significant bit must be extremely well matching (error < 1/2^(m-1)) relative to the other resistors. Since this is the smallest resistor of all the whole network would become extremely large.

Tho demonstrate the effect of tolerances in netlist RTA_tolerance.in the value of R5 (connected to D4) is modified from 1K to 1.1K. The result of this change is that when bit D4 changes the conversion becomes non monotonic.


Fig. 3: Loss of monotony due to resistor tolerances.

The same sensitivity applies to the voltage at input D4.

Conclusion