Electronics - Analog and Digital Converters - Discussion

Analog output for the input code 0101.

Formula: Va = Vref / 2^n * input code bit (Start from MSB).
Given : Vref = 5V; Input code bit = 0101.

Va = (Vref / 2^0 * 0) + (Vref / 2^1) * 1) + (Vref / 2^2 * 0) + (Vref / 2^3 * 1).
Va = (5 / 1 * 0) + (5 / 2 * 1) + (5 / 2^2 * 0) + (5 / 2^3 * 1).
Va = (5 / 1 * 0) + (5 / 2 * 1) + (5 / 4 * 0) + (5 / 8 * 1).
Va = (0) + (2.5) + (0) + (0.625).
Va = 3.125 V.

@Vidya.

R2r ladder has resolution =Vr/2^n (only).

Here Vref=+5 and the input is 0101(means 4 bit DAC).
In a 4-bit binary system, values should be 0000 to 1111 means 0 to 15 (or F).
As the R-2R ladder is connecting to inverting terminal of the Op-amp the output analog value will be ranging from 0V to -5V.

If the input is 0000 the output = 5 (0)/15 = 0 V.
If the input is 1111 the output = 5 (15)/15 = -5 V.

Here we have 0101 means 5.

So, output = -5 * 5/15 = -1.66 V.

The correct equation for 4 bit DAC should be,

Vo = -R(b3 * 2^3 + b2 * 2^2 + b1 * 2^1 + b0 * 2^0).
= -R (b3 * 8+b2 * 4+b1 * 2+b0 * 1)
Here R = Resolution = Vref/(2^n) - 1.
Correct me if I am wrong.

Formula = Vref/2^n(msb bit * 2^0 + nextbit * 2^1 + nextbit * 2^2 + lsb bit * 2^3).

Yes,

Actual answer is 1.5625 volts.

Given in the sum is reference voltage = 5v, and resolution = 4.

So voltage per lsb = vref/2^n = 5/2^4 = 0.3125 v/lsb.

Therefore = 0101 in decimal is 5 = 5*0.3125 = 1.5625.

In case of inverting, Vo = -1.5625 V.

In case of non-inverting, Vo = 3.125V.

So the given answer is correct.

Vo = (Rf/R)(Vref)(Do/16+D1/8+D2/4+D3/2).

MOST EASY METHOD:

V(0ut) = (Vi/8)*digital input.

@Nirja.

Formula = (Vref/2^N)(dec equivalent of i/p).

N- is number of significant bits (here 3 as msb is 0).

Here 0101 = 101 hence consider 3 bit.

Therefore,
Vo = 5(Vi/8) = 3.12.

Formula = [Vref/(2^n)] {msb bit * 2^0 + next bit * 2^1 + next bit * 2^2 + lsb bit * 2^3}.

Where n = no of bit,

Solution:

Vref = 5v;
n = 4;

=> (5/(2^4)) {0*0 + 1*2 + 0*4 + 1*8}

=> (5/16) {0 + 2 + 0 + 8}

=> (0.3125) {10}

=> 3.125.

Answer => 3.125.