Precision Rectifiers using Op-amp

Precision Rectifiers

May-04,11 Dec.-05, 06, 07,09

Recall from basic circuit principles that a rectifier circuits can be implemented with a diode/diodes (half wave rectifier or full wave rectifier). The major limitations of these circuits is that they cannot rectify voltages below V_D(ON) = 0.7 V, the cut-in voltage of the diode. In these circuits V; has to rise to a threshold of the order of VD(ON) before any appreciable change can be seen at the output.

Therefore, above this threshold we have V_o = V_i - V_D(ON) threshold V_i= 0.7 V and below i.e. threshold V_o= 0 i.e.

V_o = V_i - V_D(ON)  for V_i  ≥ V_D(ON) … (3.27.1.(a))

V_o = 0 V  for V_i   ≤ V_D(ON) … (3.27.1.(b))

Due to this, output of the conventional rectifier is distorted, as shown in the Fig. 3.27.1.

To achieve precision rectification we need a circuit that keeps V_o equal to V_i for V_i > 0V. This can be achieved by using op-amp along with the diodes and these circuits are called precision rectifiers. These are used to precisely rectify voltages having amplitudes less than 0.7 V. Hence these circuits are called small signal precision rectifiers.

1.  Precision Half Wave Rectifiers

The precision half wave rectifiers are classified as,

1. Positive half wave rectifier 2. Negative half wave rectifier

a. Positive Precision Half Wave Rectifier

The Fig. 3.27.2 shows the positive small signal precision half wave rectifier.

The diode D₁ is used in the feedback loop of the circuit. The analysis can be done for V_i > 0 V and V_i < 0 V.

Case 1 : V_i > 0 V

Consider that input voltage is positive going. Due to high open loop gain of op-amp it produces high voltage VOA. This provides enough drive to the diode D1 to make it forward biased. So it acts as a ideal diode and in forward biased condition behaves as a switch as shown in the Fig. 3.27.3.

The cut-in voltage of diode of 0.7 V gets divided by A_OL which is very high. Hence immediately when V_i starts increasing, D₁ becomes ON.

Then circuit works as a voltage follower. From virtual ground V_n = V_p = V_i and V_o = V_n due to the feedback path. Hence entire positive half cycle is available across the load.

Case 2 : V_i < 0 V

When V_i goes negative, immediately VOA produced attains - Vsat value making diode Di reverse biased. Thus diode D1 acts as an open circuit as shown in the Fig. 3.27.4.

Due to OFF diode D₁, feedback path gets opened and no current can flow through RL. The voltage V_o is 0 V and negative half cycle of V_i gets clipped from the output. 

The input-output waveforms are shown in the Fig. 3.27.5.

Thus compared to conventional rectifiers, precision rectifiers can rectify very small voltages of the order of few millivolts.

Key Point For positive input cycle, the positive output cycle exists at the output hence the circuit is also called non-inverting half wave precision rectifier.

b. Negative Precision Half Wave Rectifier

By changing the direction of D₁ in positive half wave rectifier circuit, the negative half wave rectifier can be obtained. It is shown in the Fig. 3.27.6.

When V_i  > 0 V i.e. positive going, immediately VOA is very high due to high open loop gain. This reverse biases the diode, making it open. Thus V_o = 0 V as no current can pass through R_L.

When V_i < 0 V i.e. negative going, instantaneously V_OA is highly negative which forward biases the diode Dx making it ON. It acts as short circuit and the circuit acts as a voltage follower. Hence the output voltage is same as input voltage. Thus the entire negative half cycle is available across the load. Hence the circuit is called negative half wave rectifier. The waveforms are as shown in the Fig. 3.27.7. 

Another type of negative half wave rectifier which acts as an inverting precision half wave rectifier is shown in the Fig. 3.27.8.

The basic op-amp circuit is used in inverting mode and the input is applied to inverting input terminal. When V_i  > 0 V i.e. positive going, due to high open loop gain VOA is highly negative.

This forward biases the diode D₁ and reverse biases D₂ and circuit becomes as shown in the Fig. 3.27.9.

Thus it acts as an inverting amplifier as feedback path gets established through ON diode D₁.

Vo = - (R_f / R₁) V_i

Using R_f = R₁,V_o = -V_i

Thus for positive half cycle of the input, negative half cycle is available at the output.

When V_i < 0 V, immediately V_OA becomes highly positive due to which D2 becomes forward biased and Df reverse biased. As D₁is OFF; V_o = 0 V while diode D₂ prevents op-amp to go into the positive saturation. The circuit is shown in the Fig. 3.27.10.

Key Point As negative half cycle is produced for positive half cycle of the input, the circuit is called the inverting half wave rectifier.

The waveforms are shown in the Fig. 3.27.11. 

2. Precision Full Wave Rectifiers

The full wave rectifier circuits accept an a.c. signal at the input, inverts either the negative or the positive half, and delivers both the inverted and non-inverted halves at the output, as shown in the Fig. 3.27.12.

The operation of the positive full wave rectifier is expressed as,

V_o = | V_i |    ... (3.27.2)

And that of the negative rectifier as

V_o = | V_i |    ...(3.27.3)

Looking at equations (3.27.1) and (3.27.2) we can say that precision full wave rectifier circuits are precision absolute value circuits. Fig. 3.27.13 shows a full wave rectifier or absolute value circuit.

CASE 1 : V; > 0 : When V_i > 0, inverting side of A₁ will force its output to swing negative, thus forward biasing D₁ and reverse biasing D₂. Since no current flows through resistance R connected between V_n1 and V_p2, both are equipotential.

i.e. V_n1 = V_p2 = 0V

The Fig. 3.27.14 shows the equivalent circuit.

From equivalent circuit, the output voltage can be given as,

V_o = (-R / R) – (R / R) V_i = V_i   ….. (3.27.4)

CASE 2 : V_i < 0 : When V_i < 0, negative, the output voltage of A1 swings to positive, making diode D₁ reverse biased and diode D₂ forward biased.

The Fig. 3.27.15 shows the equivalent circuit.

Let the output voltage of op-amp A1 be V. Smce the differential input to A 2 is zero, the inverting input terminal is also at voltage V, as shown in the Fig. 3.27.15.

Applying KCL at node 'a' we have

To find Vo interms of V we concentrate on the equivalent circuit of A2, as shown in the Fig. 3.27.16.

Substituting value of V in above equation we get,

Hence for V_i < 0 the output is positive. This is illustrated in Fig. 3.27.17.

Review Questions

1. Explain the need of precision rectifiers.

2. Draw the circuit and explain  the working of precision half wave positive rectifier.

3. Draw the circuit and explain the working of precision half wave negative rectifier.

4. Draw the circuit and explain the working of precision full wave rectifier.