Analog Circuit--Miscellaneous Talk on Rectification

Analog circuit textbooks usually talk about rectifier circuits, but they are usually very brief, only one or two pages long, and they often only talk about the most common rectifier circuits in low-power electronic equipment. Some textbooks even only talk about bridge rectification and not full-wave rectification circuits.

In fact, the rectifier circuit looks simple, but the changes and calculations inside are quite complex.

The simplest rectifier circuit is a half-wave rectifier circuit, as shown in Figure 01. Strictly speaking, Figure 01 includes the capacitor at the rectifier output end, which is already a rectifier filter circuit.

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However, this simplest half-wave rectifier circuit has some problems, and its transformer requires special design. It is probably for this reason that the fourth and fifth editions of Kang Huaguang's "Fundamentals of Electronic Technology. Analog Part" do not talk about half-wave rectifier circuits, avoiding this problem.

Regarding the operation of the half-wave rectifier transformer, we will discuss it in detail later, but we will put it aside for now.

Figure 02 is the so-called full-wave rectifier circuit, which can be seen as a combination of two half-wave rectifier circuits composed of two secondary windings of the same transformer. Windings A1 and A2 have the same number of turns and are wound on the same iron core. The polarity of the two windings is as shown in the figure. In fact, winding A1 and winding A2 are one winding, and the connection point is the center point of this winding, or called the center tap.

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In the half cycle of power frequency AC, assuming that the end of the winding point is positive, winding A1 works, but winding A2 has no current flowing due to the reverse direction of diode D2, and A2 seems to not exist during this half cycle. In the second half of the cycle, the direction of the AC voltage is opposite, winding A2 works, and A1 has no current due to the reverse direction of diode D1. Therefore, windings A1 and A2 work alternately during the two half-cycles of AC. During the half-cycle, A1 and A2 work the same as half-wave rectification. So we can say that full-wave rectification is composed of two half-wave rectifications composed of two secondary windings of the same transformer.

If the two diodes of the full-wave rectifier circuit in Figure 02 are reversed, it will become the circuit in Figure 03.

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The only difference between the circuit in Figure 03 and the circuit in Figure 02 is that in Figure 02 the negative end of the load ZL is connected to the center point of the secondary winding of the transformer, while in Figure 03 the positive end of the load is connected to the center point of the secondary winding of the transformer.

The rectifier circuit in Figure 02 can be called positive full-wave rectification because the negative terminal of the load is connected to the center point of the secondary winding. The rectifier circuit in Figure 03 can be called negative full-wave rectification because the positive end of the load is connected to the center point of the secondary winding.

Put the positive full-wave rectifier circuit in Figure 02 and the negative full-wave rectifier circuit in Figure 03 together, as shown in Figure 04

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We find that although the rectifier circuit on the right is different, the transformers are exactly the same.

Then we cut out the left half of the transformer of the negative full-wave rectifier circuit in Figure 03:

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Then paste it into the positive full-wave rectifier circuit in Figure 02, and connect the three points C, E, and D with the three points A, E, and B to form the circuit in the upper part of Figure 06. It has both positive full-wave rectification output and negative full-wave rectification output. In other words, this is a power supply with positive and negative outputs, and the positive and negative output voltages are equal.

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If you look carefully at the positive and negative full-wave rectifier circuit in the upper part of Figure 06, it is exactly the same as the circuit in the lower part of Figure 06.

However, the circuit below in Figure 06 is by no means a bridge rectifier circuit, it is just similar in appearance. The circuit below Figure 06 is a combination of two full-wave rectifier circuits.

If the negative power load of the lower circuit in the figure is disconnected, there will be only upward current in winding A1 and only downward current in A2. If the positive supply load is disconnected, then there will be only downward current in winding A1 and only upward current in A2. It can be seen that the rectifier circuit below Figure 06 is not a bridge rectifier circuit, but a combination of two full-wave rectifier circuits.

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In addition to very simple and rough loads such as DC motors, the rectifier circuits in electronic equipment need to be matched with filter circuits. The rectified voltage and current can be used by electronic equipment after being filtered.

The picture above is a typical circuit of full-wave rectifier capacitor filtering. In the figure, C is the filter capacitor, and ZL represents the load.

If we connect an oscilloscope to both ends of the filter capacitor C, we will see a waveform like the following.

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The voltage across the capacitor C fluctuates, and this fluctuation is generally called ripple.

If we use a dual-trace oscilloscope, and the other channel is connected to point M in Figure 01, and the two channels use the same sensitivity, then the voltage waveforms of the two channels are as follows:

We can see that the voltage across winding A1 (black) has a section near the peak value that is close to coinciding with a "bulge" on the ripple (blue).

The blue curve is the voltage across capacitor C, and the voltage across C rises at the "bulge". A rise in the voltage across the capacitor indicates that the capacitor is being charged. Where does this charging current come from? Obviously, it is because the instantaneous value of the voltage across winding A1 exceeds the voltage across the capacitor, so winding A1 charges capacitor C through rectifier diode D1.

When the voltage across winding A1 passes through the maximum point and drops below the voltage across capacitor C, winding A1 will of course not charge the capacitor. At this stage, the capacitor discharges to the load, and the voltage at both ends gradually decreases.

From the time relationship between the voltage waveform at point M and the voltage waveform across the capacitor, we can imagine that the "bulge" on the voltage waveform at both ends of the capacitor when the voltage waveform at point M is at its valley value (maximum value in the opposite direction) is the N point of the other half of the winding A2. Diode D2 charges capacitor C.

If we use a more trace oscilloscope and can measure the current, then the relationship between the multi-current waveform at the midpoint K of the secondary winding of the transformer, the electromotive force of the winding, and the voltage across the capacitor is shown in Figure 04:

The blue curve in the figure is the voltage across the capacitor C, and the red curve is the current from the ground wire to the midpoint K of the transformer.

In order to analyze the work of the full-wave rectifier capacitor filter circuit, we add annotation symbols in Figure 04, as shown in Figure 05.

In the analysis of Figure 05, we assume that the diode is an ideal diode with zero forward voltage drop.

In Figure 05, the black curve is the electromotive force (open circuit voltage) of the two half secondary windings, not the terminal voltage of the two half windings. The part of the electromotive force curve below the horizontal axis is not drawn. The blue curve is the voltage across the capacitor C, and the red curve is the current in the two half windings.

Taking any half of the power frequency cycle, before time t1, the electromotive force of the secondary winding of the transformer is less than the voltage across the capacitor, there is no current in the two diodes, and the load relies on capacitor discharge to maintain the current in it. At time t1, the electromotive force of the winding begins to be greater than the voltage across the capacitor. Winding A2 charges capacitor C through diode D2, and the red curve begins to rise. As the electromotive force of the secondary winding increases, the current also increases rapidly, and the voltage across the capacitor increases. During the period from t1 to t2, the secondary winding not only charges the capacitor, but also supplies power to the load. When the electromotive force of the secondary winding begins to decrease, the charging current decreases rapidly. When the electromotive force of the secondary winding is lower than the voltage across the capacitor, charging stops and the current in the secondary winding is zero. After time t2, the capacitor discharges to the load to maintain the current in the load, and the voltage across the capacitor decreases.

In the figure, we can see that during the period from t1 to t2, the electromotive force of the winding and the voltage across the capacitor are slightly different, and the black curve is slightly higher than the blue curve. This is because the winding always has a certain resistance, which will drop part of the voltage, and the greater the current in the winding, the greater the voltage drop. The difference between the two curves is the voltage drop across the winding resistance.

In the second half of the power frequency cycle, the aforementioned process is repeated, except that in the second half of the cycle, winding A1 and diode D1 start charging the capacitor at time t3 and end at time t4. There is no current in the winding from time t2 to time t3, and the current in the load is maintained entirely by the capacitor discharging into the load.

The two half secondary windings A1 and A2 alternately charge the capacitor through the diode, and then the capacitor discharges the load. This is the working process of full-wave rectification capacitor filtering.

We see that in the capacitive filter circuit, the current in the transformer winding is intermittent, with relatively narrow pulses. The current is discontinuous and in the form of pulses, which is a characteristic of capacitive filtering.