Application of Junction Diode as a Rectifier

Figure 14.18 is the first rectifier circuit a student meets, and it teaches a simple but profound idea: a single diode can convert an alternating voltage into a unidirectional (but still pulsating) voltage. The figure has two panels, (a) and (b), and you must read them together.

Panel (a) shows the circuit. A transformer steps the mains ac voltage up or down as needed; its secondary winding has two terminals labelled A and B. Terminal A is connected to the anode of a single diode. The cathode of that diode connects to one end of a load resistor $R_L$. The other end of $R_L$ returns to terminal B, completing the loop. That is the entire circuit — one diode, one resistor, and a transformer. There is no centre tap, no second diode, no capacitor.

Panel (b) shows two waveforms stacked vertically, both plotted against time on the horizontal axis. The upper waveform is the input ac voltage across the secondary (between A and B). It is a pure sinusoid: it rises smoothly from zero to a positive peak, falls back through zero, goes to a negative peak of equal magnitude, and returns to zero — one full cycle. The lower waveform is the output voltage measured across $R_L$. Here the negative half-cycles are completely absent; the output is zero during those intervals. Only the positive half-cycles appear, each shaped like the top half of a sine wave — a series of humps separated by flat zero segments. The output is therefore a train of positive pulses, one per input cycle.

The physical idea is straightforward. A diode conducts only when forward biased (anode positive with respect to cathode). During the positive half-cycle of the input, terminal A is positive relative to B, so the diode is forward biased and current flows through $R_L$, producing a voltage drop across it. During the negative half-cycle, A is negative relative to B, the diode is reverse biased, and the reverse saturation current is so small (essentially zero for practical purposes) that no appreciable current flows. Hence the output voltage is zero. The diode must be chosen so that its reverse breakdown voltage exceeds the peak input voltage; otherwise it would be destroyed during the reverse-biased half-cycles. …

Fig. 14.19 is the centre-piece of the full-wave rectifier discussion. It packs three panels into one figure, and each panel teaches a different part of the story: the circuit topology, the two out-of-phase inputs, and the resulting output.

Panel (a) shows the circuit. A centre-tapped transformer secondary gives two equal voltages, one from the centre tap to terminal A and one from the centre tap to terminal B. Two diodes, D1 and D2, have their p-sides connected to A and B respectively. Their n-sides are joined together at a common node. The load resistor $R_L$ is connected between that common node and the centre tap. This is the defining feature of a centre-tap full-wave rectifier: the load sees the voltage from the common cathode point to the centre tap, so each diode conducts on alternate half-cycles and the current through $R_L$ always flows in the same direction.

Panel (b) shows two input voltage waveforms, one at A and one at B, plotted against time. The key point is that they are $180^\circ$ out of phase. When A is positive with respect to the centre tap, B is equally negative, and vice versa. This phase relationship is what allows the two diodes to take turns conducting.

Panel (c) shows the output voltage across $R_L$. It is a train of positive half-sinusoid humps, one for every half-cycle of the input — there is no gap. During the half-cycle when A is positive, D1 conducts and the output follows the positive half of the A waveform. During the next half-cycle, B is positive, D2 conducts, and the output follows the positive half of the B waveform. The result is a full-wave rectified voltage: unidirectional but still pulsating, with a frequency twice that of the input.

Because both halves of the ac cycle now contribute a pulse to the output, a full-wave rectifier delivers a steadier, more efficient output than a half-wave rectifier for the same transformer — the output pulses are twice as frequent and the gaps between them are gone. The output in panel (c) is still not steady dc, though; like the half-wave case, it still has significant ripple, which is why the textbook follows this figure with a discussion of the capacitor filter (Fig. 14.20) to smooth it into something close to steady dc. …

Fig. 14.20 is the textbook’s way of showing you how a simple capacitor turns the bumpy, pulsating output of a full-wave rectifier into a much smoother, nearly steady dc voltage. The figure has two panels, (a) and (b), and you need to understand both to see the full story.

Panel (a) is the circuit diagram. It is exactly the full-wave rectifier from Fig. 14.19 — two diodes $D_1$ and $D_2$, a centre-tapped transformer, and a load resistor $R_L$ — but now with one extra component: a capacitor $C$ connected in parallel across $R_L$. This capacitor is the filter. It sits directly across the output terminals, so the same voltage that appears across $R_L$ also appears across $C$. The textbook calls this a capacitor-input filter because the rectified voltage first “sees” the capacitor before the load.

Panel (b) is actually TWO separate stacked panels sharing the same time axis, not a single plot -- confirmed against the real page. The TOP panel, labelled “ac input,” simply re-draws the original ac source waveform: a plain, undistorted sine wave, swinging equally positive and negative, identical in shape to the input waveform in Figs 14.18 and 14.19. It is not a rectifier output at all -- it is shown so you can compare the filtered output's ripple rate against the original ac cycle. The BOTTOM panel, labelled “output with capacitor input filter,” is where the capacitor's effect is actually shown, and it is this panel -- not the whole of (b) -- that carries two curves on one set of axes. The dashed curve shows the output of the full-wave rectifier without the filter — the familiar train of half-sinusoid humps, one for each half-cycle of the ac input, touching zero between humps. This is the pulsating dc that the rectifier alone produces. The solid curve shows the voltage across the capacitor (and therefore across $R_L$) with the filter in place. This solid line is the smoothed output: it rises quickly with the first hump, charging the capacitor to nearly the peak voltage, and then, as each rectified hump falls back toward zero, the capacitor discharges slowly through $R_L$ instead of following it down, producing a shallow downward droop; the next hump recharges the capacitor back to the peak before it can droop far, and the cycle repeats. The result is a voltage that stays close to the peak value throughout, with only a small periodic variation called the ripple -- the shallow sawtooth-like dips on the solid curve, spaced at twice the input frequency (once per rectified hump).

The physical idea is straightforward: the capacitor stores charge when the rectified voltage is high, and releases that charge to the load when the rectified voltage drops. This “fills in the gaps” between the humps. Without the capacitor, the output falls to zero between humps; with the capacitor, it never falls that low. The quality of the smoothing depends on how slowly the capacitor discharges, which is governed by the time constant $\tau = R_L C$.

The ripple voltage itself can be estimated. If the capacitor discharges approximately linearly (a good approximation when the ripple is small), the charge lost during one discharge interval $\Delta t = 1/(2f)$ is $\Delta Q = I_{\text{load}} \Delta t$, where $I_{\text{load}} \approx V_{\text{peak}}/R_L$ is the average load current. The corresponding voltage drop (the ripple) is

This formula is not given explicitly in the textbook text you provided, but it follows directly from the physics of capacitor discharge and is the standard result for a full-wave rectifier with a capacitor filter. A larger $C$ or a smaller load current (larger $R_L$) gives a smaller ripple — a smoother dc output. …