AN2615 datasheet(9/37 Pages) STMICROELECTRONICS

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AN2615

Circuit analysis

9/37

Circuit analysis

In this analysis, it is assumed that there is no noise present and the i/p offset voltage of the

op-amp is negligible.

I = (V1 – Vin)/R = C * dVc/dt

Where, Vc = Vout – V1 and current ‘I’ is constant for a given input.

Applying the Laplace transform:

(V1 – Vin)/s * R = C * (s Vc(s) – Vc (0+))

or,

(V1 – Vin)/s

2 = (R * C) * ( V

c (s) - Vc(0+)/s)

Applying the inverse Laplace transform, we get

(V1 – Vin) * T = (R * C) * ( Vc(t) - Vc(0+) )

------------------- (1)

As shown in Figure 3: Timing diagram on page 8

At T = T2, Vc(T2) = V2 – V1

And, at T =T3, Vc (T3)= V3 – V1

So,

(V1 – Vin) * T2 = (R * C) * (V2 – V1 - Vc(0+))

------------------- (2)

And,

(V1– Vin) * T3 = (R * C) * (V3 – V1 - Vc(0+))

------------------- (3)

Equation (2) and equation (3) can both be used as the characteristic equation for this

converter, but factors like Vc(0+) and other constant errors remain present. But if we use

both comparators, then we can remove these factors by subtracting equation (2) and

equation (3).

After subtracting equation (2) from equation (1) and rearranging we get:

Vin = V1 - (R * C) *( V3 – V2 )/(T3 –T2)

------------------- (4)

Let measured time T3 - T2 = Tm and we get:

Vin = V1 - (R * C) * ( V3 – V2 )/Tm

------------------- (5)

By using equation (5) we can measure the value of Vin depending on the value of T3 and T2.

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