Draw and explain the function of dual slope analogue to digital converter. Derive the equations used.

Ans.              

Dual slope A/D converter: This has 4 main blocks.

a. An integrator

b. A Comparator

c. A binary counter

d. A switch driver

The conversion process at T=0 along with switch S₁ in position 0. It connects the analogue voltage Va to the input of the integrator. Therefore the output of the integrator will be as

It results in high Vc. It enables the AND Gate and the clock pulse reaches the ck input of the counter, that was firstly clear. The counter counts from 00......00 to 11.....11 while 2ⁿ -1 clock pulses are applied. At the subsequent clock pulse 2n the counter is cleared and Q will be 1. It controls the state of S₁ that now moves to position 1 at T₁, thus connecting -V_R to the input of the integrator. Here the output of the integrator starts to shift in the positive direction. The counter carries on counting until V₀ is less than 0. Immediately V₀ goes positive at T₂, V_C goes LOW disabling the AND Gate.

Wave form of dual slope A/D convertor

The time T₁ is specified by

T₁ = 2^N T_C, here T₁ is time period of clock pulse.

Once the switch S₁ is in position 1, the output voltage of the integrator is specified by

V₀ = - (Va/ τ) T₁ + (V_R/ τ)(t - T₁)

V₀ = 0 at t = T₂

Thus, T₂ - T₁  = (Va/ V_R) T₁ = (Va/ V_R)2^N T_C

Assume that the count recorded in the counter be n at T₂ thus T₂ - T₁ = n T_C =(Va/ V_R)2^N T_C

That gives n = (Va/ V_R)2^N