# 4.3 Clipping Circuits – Pulse and Digital Circuits

##### 4.3 CLIPPING CIRCUITS

Clipping circuits select that part of the signal which lies above and below a reference level. Depending on whether the diode is connected in series with the load or in shunt with the load, these circuits are called either series-clipping circuits or shunt-clipping circuits. FIGURE 4.7(a) Series clipper that clips the negative half-cycles FIGURE 4.7(b) The transfer characteristic, input waveform and output waveform of a series clipper that clips negative half-cycles

#### 4.3.1 Series Clippers

Consider the series-clipping circuit shown in Fig. 4.7(a) and its transfer characteristic (a plot that gives the relationship between the input and the output voltages) with input and output waveforms in Fig. 4.7(b). When vi is positive, D conducts and the input signal is transmitted to the output, vo = vi When vi is negative, vo = 0. There is no transmission of the signal as the diode is assumed to be ideal. The output is in the form of half-cycles, similar to the output of a half-wave rectifier; in fact, it is a half-wave rectifier.

Consider another clipping circuit shown in Fig. 4.8(a) and its transfer characteristic with input and output waveforms in Fig. 4.8(b). When vi is negative, D conducts and the input vi is transmitted to the output (i.e., vo = vi). When vi is positive, D is OFF and vo = 0. The signal is not transmitted to the output. The output once again is in the form of half-cycles.

In our discussion so far, we have assumed the diode to be ideal and have neglected the influence of the transition capacitance CT that exists between the anode and the cathode of a reverse-biased diode. We now take into account this parameter to understand how this affects the output of a series clipper. Consider the circuit shown in Fig. 4.8(a) when reverse-biased (during the positive half-cycle), to which, instead of a sinusoidal signal, a square-wave input is applied. So far we have assumed that during the period when the diode is OFF, there is no transmission. However, on account of the transition capacitance CT being present, the circuit now behaves as a high-pass circuit [see Fig. 4.8(c)] and the input can now be transmitted to the output, though with distortion. Also, even if a sinusoidal signal is applied as input, at high frequencies, the capacitor offers a smaller reactance due to which the input can be transmitted to the output. This is the major limitation of a series clipper. Thus, a series clipper works best at low frequencies. FIGURE 4.8(a) Series clipper that clips positive half-cycles FIGURE 4.8(b) The transfer characteristic, input waveform and output waveform of a series clipper that clips positive half-cycles FIGURE 4.8(c) Series clipper that is expected to eliminate positive half-cycles

Base Clipper. If a battery (VR) is included in the series-clipping circuit, such that the diode is connected in series with the load, as shown in Fig. 4.9(a), these circuits are called biased series clippers. The circuit in Fig. 4.9(a) clips the positive going input at its base, so it is also referred to as a base clipper.

Assume that the diode is ideal in the circuit shown in Fig. 4.9(a).

For vi < VR, D is OFF; hence, vo = VR. The resultant circuit is shown in Fig. 4.9(b).

For viVR, D is ON; hence, vo = vi. The resultant circuit is shown in Fig. 4.9(c).

The transfer characteristic is shown in Fig. 4.9 (d).

In the output of this circuit, the base portion of the input during the positive half-cycle is eliminated and only the positive peak is available when the input is either more than or equal to VR. Hence, the name base clipper. The battery VR is assumed to have zero internal resistance. However, in practice, any voltage source will have some internal resistance RS which appears in series with the battery. Now, as this RS in the present case appears in series with R, where R >> RS, the performance of the circuit is not affected. This could be termed as an advantage of series clippers. FIGURE 4.9(a) A base clipper FIGURE 4.9(b) A base clipper with D OFF; and (c) with D ON

Positive-Peak Clipper. Consider the circuit shown in Fig. 4.10(a). As this circuit eliminates the positive peak of the input at the output, it is called a positive peak clipper.

For vi < VR, D is ON, and the resultant circuit is shown in Fig. 4.10(b). Hence, vo = vi. And for vi > VR, D is OFF, as shown in Fig. 4.10(c). Hence, vo = VR. Thus, the transfer characteristic, the input and output waveforms are as shown in Fig. 4.10(d). In the output of the circuit, the positive peak of the input above VR is eliminated. Hence, this circuit is called a positive peak clipper. FIGURE 4.9(d) The transfer characteristic of a base clipper with input and output waveforms FIGURE 4.10(a) Positive-peak clipper FIGURE 4.10(b) Circuit of Fig. 4.10(a) when D is ON FIGURE 4.10(c) Circuit of Fig. 4.10(a) when D is OFF FIGURE 4.10(d) Transfer characteristic of a positive peak clipper in Fig. 4.10(a) with input and output waveforms

#### 4.3.2 Shunt Clippers

A shunt clipper is one in which the diode is used as a shunt element. Consider a simple shunt clipper shown in Fig. 4.11(a). As long as the input is positive, D conducts and the output vo = 0.When the input is negative, D is OFF and an open circuit. The input is transmitted to the output. The transfer characteristic, the input and output waveforms are shown in Fig. 4.11(b). This circuit clips the positive half-cycle. The same thing is done by the circuit shown in Fig. 4.8(a). The only difference is that the former is a series clipper and the latter a shunt clipper. FIGURE 4.11(a) A shunt clipper that clips the positive half-cycle FIGURE 4.11(b) The transfer characteristic, the input and output waveforms FIGURE 4.11(c) The shunt clipper in Fig. 4.11(a) when D in ON and Rf is considered

Till now we assumed that the diode to be ideal, that is, forward resistance of the diode was taken to be zero. A practical diode, however, has typically Rf in the range of 50 Ω to 100 Ω. Therefore, when D is ON, with Rf taken into account, the circuit is as shown in Fig. 4.11(c). In this circuit: vo = viRf/(Rf + R).

This means that though the output is expected to be 0, there is a small sinusoidal swing at the output. This is one limitation of a shunt clipper. When D is OFF, it should ideally behave as an open circuit. But in a reverse-biased diode, we have transition capacitance. Taking CT into account, Fig. 4.11(a) can be redrawn as shown in Fig. 4.11(d).

Now, when the diode is OFF, with a square wave as the input, we ideally expect the negative half-cycle of the input only at the output. However, when CT is considered, the shunt clipper is a low-pass circuit. Hence, the output would rise with a time constant RCT. This is another limitation of a shunt clipper. Consider an alternative form of the shunt clipper as shown in Fig. 4.12(a). The transfer characteristic along with the input and output waveforms is shown in Fig. 4.12(b). The negative half-cycle is completely eliminated as is done by the circuit in Fig. 4.7(a).

Now let us consider a slightly different shunt clipper called a biased shunt clipper that clips the positive half-cycle of the input waveform at a reference level VR [see Fig. 4.13 (a)]. For the circuit in Fig. 4.13(a), the transfer characteristic is drawn in Fig. 4.13(b).

When vi < VR, D is OFF, hence, vo = vi.

When viVR, D is ON, hence, vo = VR.

To calculate and plot the output of the clipping circuit shown in Fig. 4.13(a), consider a sinusoidal input signal varying as Vm sin ωt. FIGURE 4.11(d) The shunt clipper considering CT FIGURE 4.12(a) A shunt clipper that clips the negative half-cycle FIGURE 4.12(b) The transfer characteristic of the clipper in Fig. 4.12(a) FIGURE 4.13(a) A positive peak clipper FIGURE 4.13(b) The transfer characteristic with input and output waveforms of the circuit in Fig. 4.13(a)

Case 1

When the diode is ideal, its Rf is 0 and Rr is ∞.

vi < VR, D is OFF, vo = vi

viVR, D is ON, vo = VR

The output is as shown in Fig. 4.13(b).

Case 2 When the diode is not ideal and has finite forward and reverse resistances

1. When the diode is ON, it has a forward resistance Rf. For vi > VR the resultant circuit is as shown in Fig. 4.13(c). Here: Thus, vo is maximum when vi is maximum that is when vi = Vm.

If Vm ≈ 2VR If the source VR has an internal resistance Rs, vo(max) computed using Rf1 = (Rf + RS), instead of Rf. RS will influence the slope of the transfer characteristic. This could be another drawback of a shunt clipper.

2. When vi < VR, the diode is OFF and the reverse resistance of the diode is Rr. The resultant circuit that enables us to calculate vo is given in Fig. 4.13(d).

vo is minimum when vi is at its negative maximum, i.e., vi = −Vm ≈ −2VR. Therefore, In this case, RS of the battery will not influence the output in any way because Rr >> RS. R is chosen based on the following considerations. FIGURE 4.13(c) Circuit when D is ON and has a finite forward resistance Rf FIGURE 4.13(d) Circuit when D is OFF and has a finite reverse resistance Rr

Consider the circuit shown in Fig. 4.11(a). During the transmission period, the diode is OFF, offering a large reverse resistance Rr. For the input to be transmitted to the output terminals with negligible loss of signal, Rr should be much larger than R. This requirement says that: where a is a large number. Therefore, When the diode is ON, the output signal is small and is said to be attenuated. This condition stipulates that R should be significantly larger than Rf, the forward resistance of the diode. This requirement means From Eqs. (4.2) and (4.3): or R is chosen as the geometric mean of Rf and Rr. To illustrate how to plot the output, consider Example 4.1.

##### EXAMPLE

Example 4.1: For the clipping circuit shown in Fig. 4.13(a), VR = 10 V, Vm = 20 V, Rf = 50 Ω, R = 10 kΩ and Rr = 100 kΩ. Calculate and plot the output.

Solution: The waveforms of the clipping circuit shown in Fig. 4.13(a); (i) when the diode is ideal and (ii) when the diode has Rf = 50 Ω and Rr = 100 kΩ are plotted in Fig. 4.13(e). FIGURE 4.13(e) The input and output waveforms of the clipping circuit in Fig. 4.13(a)

The transfer characteristic in Fig. 4.13(b) is drawn on the assumption that the diode forward resistance is ideally zero. However, in practice, there is a small forward resistance Rf, which, when accounted for, will not ensure flat clipping at VR in the output, as shown in Fig. 4.13(f).

The circuit shown in Fig. 4.14(a) is a base clipper. This circuit is similar to the one shown in Fig. 4.13(a) except in the fact that the polarity of the diode is reversed here. When this is done, the positive peak clipper becomes a base clipper.

For the circuit in Fig. 4.14(a), the transfer characteristic is drawn in Fig. 4.14(b).

When vi < VR, D is ON and vo = VR.

When viVR, D is OFF and vo = vi. FIGURE 4.13(f) The transfer characteristic and output, considering Rf FIGURE 4.14(a) A base clipper FIGURE 4.14(b) The transfer characteristic of the circuit in Fig. 4.14(a) with input and output

There can be many variations of one-level clippers. The relevant one level shunt- and series-clipping circuits along with transfer characteristics and output waveforms are summarized in Figs. 4.15(a) and Fig. 4.15(b) respectively, with a sinusoidal signal as input.

Clipping circuits are used to either select or eliminate a part of the waveform. As an example, consider the output of a low-pass circuit for a square-wave input as shown in Fig. 3.7(b). When τ is small, the output rises exponentially to reach V or V, resulting in a distortion in the shape of the signal at the output. If a perfect square wave though with smaller amplitude is needed, we can eliminate the exponential part of the output by using peak clippers. Another example could be an astable multivibrator, where, as we shall see later, the square wave generated may not have sharp rising edges. If the astable multivibrator is required to derive a perfect square wave, we can use peak clippers. Similarly circuits shown in Figs. 2.21(a) and 2.21(b) are used to eliminate negative and positive spikes respectively. Depending on the requirement, we can use either a specific clipper or a combination.

#### 4.3.3 Two-level Clippers

We have considered clippers which clip the input at one level. Let us now consider clippers which clip the signal at two independent levels. Two diode clippers may be used in a cascade to limit the output at two independent levels. If a positive-peak clipper and a negative-peak clipper are used in a pair, the resultant circuit is called a two-level clipper. If the positive and negative peaks are clipped at the same level, the two-level clipper is called a limiter. On the other hand, if a positive-peak clipper and a positive-base clipper are connected in tandem, the circuit is called a positive slicer.

Slicers. The input can be clipped at two independent levels, either during the positive going half-cycle or during the negative going half-period. If the input is clipped at two levels during the positive going half-cycle, leaving only a slice of the input at the output, the circuit is called a positive slicer. If on the other hand, the signal is sliced during the negative half-cycle, the circuit is called a negative slicer. FIGURE 4.15(a) One-level shunt clippers

Positive Slicers: The circuit shown in Fig. 4.16(a) is a positive slicer, as it slices the positive going signal at two independent levels.

Consider the following conditions:

1. When vi < VR1, D1 is ON, D2 is OFF. The circuit in Fig. 4.16(a) reduces to that in Fig. 4.16(b). From Fig. 4.16(b), vo = VR1.
2. When VR1 < vi < VR2, D1 and D2 are OFF. Hence, the resultant circuit is shown in Fig. 4.16(c). From Fig. 4.16(c), vo = vi.
3. When vi > VR2, D1 is OFF and D2 is ON. Hence, the circuit reduces to that shown in Fig. 4.16(d). Hence, vo = VR2. Figure 4.16(e) represents the transfer characteristic, input and output of a positive slicer. We observe that in the output only a portion of the positive going signal is selected. FIGURE 4.15(b) One-level series clippers FIGURE 4.16(a) A positive slicer FIGURE 4.16(b) The circuit of Fig. 4.16(a) when D1 is ON and D2 is OFF

Negative Slicers: To implement a negative slicer, consider the circuit shown in Fig. 4.17(a).

Consider the following conditions

1. When vi ≤ −VR1, D1 is ON, D2 is OFF. Hence, the circuit reduces to that shown in Fig. 4.17(b). Therefore, vo = −VR1.
2. When VR1 > vi >VR2, D1 and D2 are OFF. The resultant circuit is shown in Fig. 4.17(c). Hence, vo = vi FIGURE 4.16(c) The circuit of Fig. 4.16(a) when D1 and D2 are OFF FIGURE 4.16(d) Circuit of Fig. 4.16(a) when D1 is OFF and D2 is ON FIGURE 4.16(e) The transfer characteristic of a positive slicer with input and output waveforms

3. When vi ≤ −VR2, D1 is OFF and D2 is ON, the resultant circuit is shown in Fig. 4.17(d). Hence, vo = −VR2. The transfer characteristic is plotted in Fig. 4.17(e). We see that in the output only a portion of the negative going signal is selected.

Limiters. The combination of a positive-peak clipper and a negative-peak clipper, clipping the input symmetrically at the top and the bottom is called a limiter as shown in Fig. 4.18(a). Consider the following conditions: FIGURE 4.17(a) A negative slicer FIGURE 4.17(b) The circuit of Fig. 4.17(a) when D1 is ON D2 is OFF FIGURE 4.17(c) The circuit of Fig. 4.16(a) when D1 and D2 are OFF FIGURE 4.17(d) The circuit of Fig. 4.17(a) when D1 is OFF and D2 is ON FIGURE 4.17(e) The transfer characteristic of the negative slicer with input and output waveforms

1. When −VR < vi < VR, D1 and D2 are OFF and the resultant circuit is shown in Fig. 4.18(b).
Hence, vo = vi.
2. When viVR, D1 is ON and D2 is OFF. Under this condition, the resultant circuit is shown in Fig. 4.18(c).
Hence, vo = VR.
3. When vi ≤ −VR, D1 is OFF, D2 is ON. The circuit that is to be considered is shown in Fig. 4.18(d).

Hence, vo = −VR. The transfer characteristic of the limiter is as shown in Fig. 4.18(e). FIGURE 4.18(a) A limiter FIGURE 4.18(b) The circuit of Fig. 4.18(a) when both D1 and D2 are OFF FIGURE 4.18(c) The circuit of Fig. 4.18(a) when, D1 is ON and D2 is OFF FIGURE 4.18(d) The circuit of Fig. 4.18(a) when D1 is OFF, D2 is ON FIGURE 4.18(e) The transfer characteristic of a limiter with input and output waveforms FIGURE 4.19(a) A limiter using Zener diodes and (b) the transfer characteristic

The limiter circuit can also be implemented using Zener diodes as shown in Fig. 4.19(a).

When −(Vz + Vγ) < vi < (Vz + Vγ),         vo = vi

When vi ≥ (Vz + Vγ),        vo = (Vz + Vγ)

When vi ≤ −(Vz + Vγ),         vo = −(Vz + Vγ)

The transfer characteristic is drawn in Fig. 4.19(b). Limiters are used in frequency-modulated systems where only the frequency of the carrier is varied, but its amplitude remains constant.

Two-level Emitter-coupled Transistor Clipper. The circuit shown in Fig. 4.20(a) is a two-level emitter-coupled transistor clipper. Let the input vi to Q1 be small enough (< vi1) to keep Q1 OFF. As a result, IC1IE1 = 0. If VBB is adjusted such that Q2 is in the active region, then the voltage vo = VCCIC2RC. When vi is increased further so that Q1 conducts, there is IE1 through Re, the drop across Re increases which in turn reduces IB2 of Q2 resulting in reduction of IC2. Consequently, vo increases. When vi is increased further, vo also rises. Thus, the output is proportional to the input in a limited region. A further increase in vi to vi2 enables Q1 to draw reasonably large IE1 and the drop across Re can now reverse-bias the base−emitter diode of Q2, thereby driving Q2 into the OFF state. As a result, vo is limited to VCC. The transfer characteristic with input and output waveforms is shown in Fig. 4.20(b). Thus, this circuit behaves as a two-level clipper (slicer). The region of linearity can be controlled by the choice of VBB. FIGURE 4.20(a) A two-level transistor clipper

#### 4.3.4 Noise Clippers

If an input signal has an associated noise component, it will cause the signal amplitude to fluctuate. This noise component may sometimes trigger sensitive circuits. Now, consider Figs. 4.21(a) and (b) which represent two input signals with associated noise components.

Series and Shunt Noise Clippers. An input signal with noise components seen in Fig. 4.21(a), can be eliminated by a series noise clipper shown in Fig. 4.21(c). As long as the noise magnitudes are small (< |Vγ|), the diodes are OFF. Hence, the output is zero during the period noise is present. The output is devoid of noise. Now let the input signal have an associated noise as represented in Fig. 4.21(b). This noise can be eliminated by a shunt noise clipper, as shown in Fig. 4.22(a). FIGURE 4.20(b) The transfer characteristic of a two-level transistor clipper with input and output waveforms FIGURE 4.21(a) An input signal with an associated noise FIGURE 4.21(b) An input signal with an associated noise

Here, the magnitude of the output is limited to VF, the forward voltage of the diode and noise is eliminated in the output. If only the noise is to be eliminated, the diodes can be biased by an appropriate voltage, V [see Fig. 4.22 (b)]. FIGURE 4.21(c) A series noise clipper FIGURE 4.22(a) A shunt noise clipper FIGURE 4.22(b) A biased noise clipper

Compensation for Changes with Temperature. We know that Vγ reduces by approximately 2.5 mV/°C rise in temperature. Consequently, the output of the clipping circuit can change. Compensation techniques may be employed in precision clipping circuits to take care of variation in Vγ by temperature changes. Let us consider the series clipping circuit in Fig. 4.23(a).

If the diode is ideal, this is simply a switch. But an idealized diode is represented by an ideal diode in series with Vγ; hence the above circuit is redrawn as shown in Fig. 4.23(b). If Vγ now changes, the output will also change accordingly. To make sure that the output does not vary with temperature, the circuit shown in Fig. 4.23(c) may be employed.

The two diodes D1 and D2 are identical, which means that the variation of Vγ with temperature, is identical in both the diodes; hence, changes in temperature will not alter the output. However, D2 should be always ON. For this, V1 and R1 are provided to forward-bias D2. The need for a separate source V1 may be eliminated as shown in Fig. 4.23(d). Here D2 is kept ON by VR and R1. Figure 4.23(e) presents a modification of this circuit. FIGURE 4.23(a) A base clipper FIGURE 4.23(b) A base clipper with a practical diode FIGURE 4.23(c) A base clipper with a temperature compensation FIGURE 4.23(d) A base clipper with temperature compensation with no need for the source V1 FIGURE 4.23(e) A modified base clipper

As long as vi < VR, D1 is OFF, D2 is ON, vo = VRVγ.

If vi > VR, D1 is ON, D2 is OFF, vo = viVγ.

Thus, temperature compensation can be provided in other diode clipping circuits on similar lines.