Question

Design a 5-bit DAC using op-amp adder. Specify the minimum op-amp supply voltage
required for proper operation. Calculate the step size for digital input of 0-5 V. What is %
error of DAC if the error is _+LSB?

Answer 1

See the diagram.

5-bit DAC. We have resistors connected to the voltages corresponding to the bits (depending on the bit position). The output resistance is R. The Opamp is connected in a negative feedback configuration.  Voltages at  the input terminals:  V₊ = V₋ = 0.

Simple current addition gives us:

[tex]V_{out} = - R\ (\frac{V_0}{16R}+\frac{V_1}{8R}+\frac{V_2}{4R}+\frac{V_3}{2R}+\frac{V_4}{R})\\\\=-\frac{1}{16}[ V_0+2V_1+4V_2+8V_3+16V_4 ]\\\\V_i=Voltage\ on\ a\ bit:\ 5V\ or\ 0V,\ \ \ Bits\ are:\ b_i\\\\V_{out}=-\frac{5}{16}[ b_0+2*b_1+4*b_2 +8*b_3+16*b_4]\\\\[/tex]


   b₄   b₃   b₂   b₁    b₀                 Vout                                     %error
   0     0     0    0      1          - 5/16   = - 0.3125 Volts                 +100%
   0     0      0   1      0          - 10/16 = - 0.6250 V                      +50% 
   0     0     0     1     1          - 15/16 = - 0.9375 V                      +33.3%

   1    1      1     1     1          - 155/16 = - 9.6875 Volts              +3.22%

The step size for the voltage = 0.3125 or 5/16 Volts.

So minimum voltage required will be 10V.

So minimum supply voltage required will be more than 10V.  Often this value is multiplied by  √2.   Then   the minimum  Vcc = +14.1 V.