##### 12.1 INTRODUCTION

When a time-varying signal, like a sinusoidal signal, is to be displayed on a CRT screen, the signal is applied to the *Y* -deflecting plates through an amplifier. However, when this time-varying signal is applied to the *Y* -deflecting plates, what we see on the CRT screen is only a vertical line, because the spot (electron beam) moves only vertically. Though this enables us to measure the peak-to-peak amplitude of the applied signal, this does not allow us to either see its shape or measure its frequency. Thus, to display a time-varying signal on the CRT screen, the spot needs to move linearly along the *X* -axis as a function of time. The sweep voltage (so called because it sweeps the spot linearly as a function of time along the *X* -axis) is applied between the pair of *X* -deflecting plates. The circuit that performs this task is called a sweep generator. A voltage sweep generator works on the principle of electrostatic deflection. The simplest sweep circuit is an exponential sweep generator in which a capacitor is allowed to charge to a supply voltage. However, the resultant sweep voltage is not necessarily linear; consequently, the spot does not always move linearly along the *X* -axis. To derive a linear sweep voltage, the capacitor needs to be charged with a constant current. The circuits that generate a linear sweep are Miller integrator and bootstrap sweep circuits. Miller integrator and bootstrap sweep circuits have negligible slope error and therefore, it can be said that these sweep generators generate a linear sweep voltage.

Let *X*_{1} − *X*_{2} be the horizontal deflecting plates of a CRO. When a voltage of the form shown in Fig. 12.1 is applied, the spot on the screen moves horizontally as the voltage varies linearly with time. As the sweep voltage falls to zero abruptly at *t*1, the spot also abruptly tries to come back to its initial position. Once again, as the voltage rises linearly, the spot also moves horizontally. This process is repeated. Due to persistence of vision, a continuous line is seen on the CRT screen. The applied voltage is called the sweep voltage.

Voltage sweep generators, which work on the principle of electrostatic deflection, are used in CROs, where a smaller deflection of the electron beam is sufficient because of the small screen. The sweep voltage so produced should vary linearly as a function of time. Only when the sweep voltage varies linearly as a function of time, the spot moves equal distances for equal increments in time along the *x* -axis. The goodness of the sweep is specified by the three errors that define deviation from linearity.

The three types of errors that define deviation from linearity are: (i) slope error or sweep speed error; (ii) displacement error and (iii) transmission error. The smaller these errors; more linear is the sweep voltage. Ideally these errors are zero for a linear sweep. Slope or sweep speed error, (*es*) is defined as the ratio of the difference between the initial and the final slopes to the initial slope, expressed as a percentage. Consider the sweep voltage as shown in Fig. 12.1(a).

**FIGURE 12.1** The sweep voltage applied to *X* -deflecting plates of a CRO

**FIGURE 12.1(a)** The waveform to calculate the slopes

**Displacement error** (*e _{d}*) is the ratio of the maximum difference between the actual sweep voltage,

*v*

_{s}, and the linear sweep, , which passes through the initial and the end points of the sweep, to the sweep amplitude, shown in Fig.12.1(b).

Transmission error (*e _{t}*): If a ramp voltage is transmitted through a high-pass

*RC*circuit, the output falls away from the input, as shown in Fig.12.1(c).

The transmission error *e*_{t} is given as:

where, *V*_{s} is the amplitude of the actual output; and is the amplitude of the linear input.

**FIGURE 12.1(b)** The waveforms to define displacement error

**FIGURE 12.1(c)** The ramp applied to high-pass circuit and the output