**Precision Full Wave Rectifier:**

The Precision Full Wave Rectifier circuits accept an ac signal at the input, inverts either the negative or the positive half, and delivers both the inverted and noninverted halves at the output, as shown in the Fig. 2.62.

The operation of the positive full wave rectifier is expressed as

and that of the negative rectifier as

Looking at equations 1 and 2 we can say that Precision Full Wave Rectifier circuits are precision absolute value circuits. Fig. 2.63 shows a full wave rectifier or absolute value circuit.

**CASE 1 : V _{i} > 0 : **When V

_{i}> 0, inverting side of A

_{1}will force its output to swing negative, thus forward biasing D

_{1}and reverse biasing D

_{2}. Since no current flows through resistance R connected between V

_{n1}and V

_{p2}, both are equipotential

The Fig. 2.64 shows the equivalent circuit.

From equivalent circuit, the output voltage can be given

**CASE 2 : V _{i} < 0 :** When V

_{i}< 0, negative, the output voltage of A

_{1}swings to positive, making diode D

_{1}reverse biased and diode D

_{2}forward biased.

The Fig. 2.65 shows the equivalent circuit.

Let the output voltage of op-amp A_{1} be V. Since the differential input to A_{2} is zero, the inverting input terminal is also at voltage V, as shown in the Fig. 2.65.

Applying KCL at node ‘a’ we have

To find V_{o} in terms of V we concentrate on the equivalent circuit of A_{2}, as shown in the Fig. 2.66.

Substituting value of V in above equation we get,

Hence for V_{i} < 0 the output is positive. This is illustrated in Fig. 2.67.