A power supply is an essential part of all electronic systems that operate from ac voltage sources. A dc power supply for small electronics consists of an ac network transformer, a rectifier and a filter.

A rectifier is the main unit, which converts ac voltage into dc voltage. Produced dc voltage is not ideal. It is the sum of a constant dc (average) value and small ac fluctuations called ripple. The filter reduces the ripple and smoothes the shape of the rectified voltage.

A stabilizer can be added when a high stability of dc voltage is required. It maintains a constant dc voltage for variations in the input voltage or in the load.

If a coil is connected to an ac source with voltage u ₁ an ac current flows through the coil and produces an ac magnetic flux Φ. It is directly proportional to the current and number of coil turns N ₁. When a second coil (winding) is placed near to the first one, the flux crosses the second coil, inducing an ac voltage u ₂ in it. The higher the number of turns N ₂, the higher the amount of induced voltage u ₂.

A device formed of two or more windings that are magnetically coupled to each other is called transformer. The coil connected to the ac source is named the primary (input) winding. A load is connected to the secondary (output) winding.

The symbol for a transformer is shown in the figure. A very important transformer feature is that there is no electrical connection between the source and the load (only a magnetic link). Transformers provide a transfer of power from one winding to another. It is an almost ideal device - the secondary power equals the primary one. The transfer ratio n of primary to secondary voltage is equal to the ratio of the number of turns in both windings.

The winding of a transformer are formed around the core. The core materials are air, ferrite and iron. The direction of the windings around the core determines the polarity of the voltages. Phase dot is used to indicate voltage polarities as shown in figure.

Construct a simple power supply circuit from the basic blocks.

The power-line (ac) voltage should be converted to dc voltage. During the positive half of the cycle, the diode is forward-biased (its anode is positive with respect to the cathode) and it allows current to flow through the circuit. During the negative half cycle, the diode is reverse biased and no current flows through the load. Since the current flows through the load only during the positive half-wave, the circuit is called a half-wave rectifier.

The rectified voltage consists of only positive waves. The upper circuit terminal is positive with respect to the lower terminal.

A Single-phase half wave rectifier is the simplest type. With a purely resistive load, the rectifier D conducts current only when the ac voltage u₂ is positive. The rectified dc voltage u_d follows the ac voltage during the positive half wave. During the negative half wave, the rectified dc voltage u_d is zero.

Average (dc) value U_d of the output voltage is calculated as U_d = U_2m/π, where U_2m is the peak value of the secondary voltage u ₂. The U_d is determined as a voltage value of a rectangular area (equal to the area of the real rectified voltage) for a period of ac supply voltage. The average value U_d is measured using a dc voltmeter.

In a single-phase rectifier, the diode is on during the positive half wave. The diode is considered ideal if the voltage across diode u_F is approximately zero. For real diodes, the forward voltage drop of from 0.7V up to 2V is often negligible compared to the applied voltage. The maximum value of reverse voltage occurs at the peak U _2m of each negative alternation in the input voltage. The diode must be capable of withstanding this amount of reverse voltage. The average current in the circuit I_d equals the diode current I_F . The average current I_d depends on the load R_L and is defined in the same way as the average voltage. A diode in a rectifier is chosen by the max reverse voltage and by the average current.

Every rectifier is produced to fulfill the user requirement for a certain dc power P_d . According to electrical laws P_d = U_d.I_d or P_d = U_d ²/ R_L .

When a rectifier circuit has to be chosen for a certain application, the transformer's mass, size and cost, should also be estimated. For each rectifier, a fixed relationship exists between transformer power rating P_TU and required output dc power P_d . For the half-wave single-phase rectifier, the transformer is designed for P_TU = 3,09.P_d. and will be huge in size even for lower powers. For this reason, this rectifier is used for low power applications - simple battery chargers, power supply units, and domestic appliances.

The simplest way to smooth the rectified voltage is to use a capacitor as a filter. This changes the rectifier's mode of operation. During the first quarter-cycle of the input voltage, the diode is forward biased. The capacitor is charged to approximately the input voltage peak.

When the input voltage begins to decrease below its peak, the capacitor holds its charge and the diode becomes reverse-biased. During the rest of the cycle, the capacitor discharges through the load at the rate determined by the R_LC time constant. The larger the time constant, the less the capacitor will discharge. Because the capacitor charges to a peak value of U_2m , the max reverse voltage of the diode is 2 U_2m .

A simple battery charger is based on a half-wave single-phase rectifier.

The rectifier determines the direction of energy flow - from power-lines to the battery. The diode is on during every positive half-wave. When the ac voltage u₂ becomes more positive than the battery voltage U_B , the resistor limits the charging current. Well-designed chargers can work without this resistor. It is also possible to use an inductor as a powerless current limiter.

It is important for battery chargers to be protected from unwanted (reverse) connection to the battery. A fuse in the ac or dc side of a charger is used for this purpose.

An inductor L connected in series to the load R_L smoothes the dc current. The rectifier appears with an inductive load and all waveforms are changed as shown in the figure.

During the positive half periods, the diode is on and a current flows through the circuit. The inductor stores electromagnetic energy proportionally to the current. When the ac supply voltage goes negative, the diode ought to turn off. Then the inductor feeds the stored energy back into the circuit. The current continues to flow in a positive direction even though the ac voltage is negative.

The rectified voltage consists of the whole positive half-wave and part of the negative. This reduces rectified voltage U_d . Thus dc voltage depends on the load R_L and inductance L.

Another practical use for a rectifier is shown in the figure. Stored inductor energy dissipates through the load and diode D ₂, which is known as a free-wheeling diode.

Even with inductance, rectifier voltage waveforms correspond to that of a rectifier with a resistive load. Rectified voltage u_d has no negative parts. The load voltage U_Load has the same average value as the rectified voltage U_d .

Current from the ac source is zero during the negative half cycle. Due to the diode D ₂, the load current decreases slowly. If the energy stored in the inductor is high enough, the current i_d never falls to zero. This mode of operation is known as continuous conduction.

The two-phase half-wave rectifier consists of two half-wave single-phase rectifiers. The second phase is formed by inverting the winding. Two ac voltages - u _2a and u _2b , produced by a transformer, supply every single rectifier. When a line voltage u ₁ is positive the secondary voltage u _2a is positive, and u _2b is negative. The diode D ₁ is on, D ₂ is off. Current flows from ac voltage source u _2a , via the diode and a load. Output voltage follows the positive half-wave of the voltage u _2a . During the negative half-wave of the line voltage u ₁ D ₂ is on and D ₁ is off. Output voltage follows positive half-wave of the voltage u _2b .

The output voltage is a sequence of half-waves with equal (positive in this case) polarity

The most popular drawing of the two-phase rectifier is known as a center tapped or full-wave rectifier. The output voltage is a sequence of half-waves with positive polarity. So the average value of rectified voltage is double that in single phase, as it shown in figure.

The diode D ₁ voltage u_F is near zero during positive half-wave of u _2a since D ₁ is on. During the negative half-wave (positive for u _2b ) D ₁ is off and D ₂ is on thus acting as a closed switch. So the cathode of D ₁ is connected to the lower point of the secondary winding. This way across D ₁ appears voltage sum (u _2a + u _2b ), which maximum value is 2U _2m .

Each diode conducts for a half period. Then the average diode current is I_FAV = I_d /2.

Including a capacitor smoothes the rectified voltage in the same way as a single-phase rectifier. This capacitive load changes the mode of circuit operation.

Diode D₁ conducts for a short time interval when a voltage u_2a becomes greater than the capacitor (rectified) voltage u_d . Diode D₂ operates in the same way with respect to voltage u_2b . When D₁ and D₂ conduct the capacitor charges, energy flows from the ac source to the capacitor and a load. During the rest of the time, the capacitor discharges through the load and holds on the relatively smooth rectified voltage.

For comparison figure shows single and two phase rectifier circuit's behavior.

A Three-phase rectifier consists like of three single-phase rectifiers. It uses a three-phase supply voltage system, which changes the mode of operation of every single rectifier.

A diode with most positive anode conducts. This diode acts as a closed switch. Thus the most positive voltage is applied to the cathodes of both rest diodes. Hence they must be off.

Therefore diodes D₁ , D₂ and D₃ conduct in sequence and current is consumed from the most positive ac supply source u_2a , u_2b or u_2c . The most positive part of voltages u_2a , u_2b and u_2c are applied to the load. The diode orientation (A - K direction) determines the direction of current flow and the positive terminal of the rectifier.

A diode voltage waveform u_F is more complicated than in a single phase rectifier. When diode D ₁ is on, the voltage drop is practically zero. When a voltage u_2b becomes more positive with respect to voltage u_2a , the diode D ₂ turns on. Then u_2a is applied to the anode and u_2b is applied to the cathode of D ₁ with respect to the common (neutral) point N of a secondary windings. During the time-interval when D ₂ is on, voltage across D ₁ is equal to the instantaneous difference (u_2a - u_2b ), which is line-to-line voltage u_2ab as it is shown in the picture. Similarly, during the time-interval when D ₃ is on, voltage across D ₁ is determined from the instantaneous difference (u_2a - u_2c ). A diode average current is I_FAV = 1/3.I_d .

Use the appropriate components to construct a single-phase bridge rectifier.

A Bridge rectifier is a full wave rectifier. It rectifies both a positive and a negative half period of a supply voltage. In order to rectify two half waves, it consists of double the diodes.

A Bridge rectifier could be single-phase, or three-phase. A two-phase rectifier is non-sense.

In bridge rectifiers, energy is consumed symmetrically from the ac supply voltage in both half periods so they have a better power utilization compared to the half-wave rectifiers.

The use of Single-phase bridge rectifiers are widely spread. They are implemented as integrated circuits.

During the positive half-wave of secondary voltage u ₂ a load current flows via D ₁ and D ₃. During negative half-wave D ₂ and D ₄ conduct current through the load in the same direction.

With pure resistive load the rectified voltage u_d consists only of positive half-waves with average value U_d . Every diode conducts a half period. Its maximum reverse voltage is U _2m and its average current is I_FAV .

The current i ₂ through the secondary winding changes its direction every half period. It is ac current. The load current i_d consists only of positive (rectified) half waves. It is dc current.

Three-phase bridge rectifier consists of 6 diodes. Three voltage sources, named secondary line voltages u _2a , u _2b , u _2c , are connected in a common (neutral) point. This circuit representation is known as Y (wye) connection.

One of the diodes D ₁, D ₃ or D ₅ is on, when its line voltage is the most positive. The most positive voltage will appear at upper rectifier terminal. Similarly the diodes D ₂, D ₄, D ₆ are on when its voltage is the most negative. The most negative voltage appears to the lower term of the rectifier. The load voltage u_d is formed by an instantaneous difference between the most positive and the most negative line voltages.

The secondary windings may be connected without a common point. This representation of a rectifier circuit is known as a Δ (delta) connection.

Each secondary voltage operates with four diodes as a single-phase rectifier. At every moment, the load current flows through two diodes. For instance, the supply voltage u _2a operates with D ₁, D ₂, D ₄, D ₅. When u _2a is the most positive, diodes D ₁ and D ₂ provide load current. When u _2a is the most negative, D ₄ and D ₅ provide. Hence, the most positive or the most negative part of each secondary voltage will be applied to the load

The only characteristic of rectifiers is output (load) characteristic. This shows the dependence of the output rectified voltage U_d versus load current I_d .

With resistive load and an ideal rectifier the output voltage U_d is unchangeable. The load current variations doesn't affect on it.

In a real rectifier, an internal resistance r_i exists. It is a sum of a diode on-resistance, resistance of transformer windings, wire resistance and similar. Because of r_i when a load current increases the rectified voltage slightly goes down.

With a capacitive or an inductive load the output voltage changes more significantly.

Each real rectified voltage consists of an ideal dc component and an ac component called ripple. Its shape depends on the rectifier circuit. The ripple is approximated with ideal sinusoidal curve, which amplitude determines so-called ripple coefficient K_{r .} This coefficient is used to estimate and compare different rectifiers.

The ripple has its own frequency - equal to or, two, three or more times higher than the line frequency depending on the rectifier. It shows how many times for a period the current path between an ac source and a load changes, or how many pulses form the load curve. Sometimes in the same manner the rectifiers are named - three-pulse, six-pulse and so on.

A single-phase bridge rectifier and two-phase or so-called centertapped rectifier are widely used in practice. Their most important features are compared in the figure.

The main disadvantages of a two-phase rectifier are the compulsory transformer with two secondary windings and high reverse diode voltage - twice as large as in bridge rectifier. These rectifiers are used for very small supply voltages (up to 10V) and high currents (over 100 A) - for example in electrochemical technologies.

Bridge rectifier is commonly used in practice. Its most important disadvantage is lacking of common connection between input and output of the rectifier.

Many analog electronic circuits require a dual voltage supply, where one of the voltages is positive with respect to zero point and another is negative, ±12V for example.

The figure shows a dual-voltage single-phase rectifier. It combines a centertapped transformer (like this in two phase rectifiers) and a bridge diode rectifier circuit.

Diodes D ₁and D ₂ form the positive voltage u_{d 1}. D ₁ conducts during positive half wave of u2a, and D ₂ - during positive half wave of u2b. In a similar way D ₃ and D ₄ forms the negative voltage u_{d 2}. The same secondary ac voltage sources u _2a and u _2b are used in forming positive and negative voltages. This guaranties equality of the two dc supplies.

Following the instructions above, construct a dual-voltage source based on three-phase rectifiers.

Construct a 12-pulse rectifier following the instructions above.

A very smooth rectified voltage could be created using the suitable sum of two "natural" six-pulse voltages. For a good result, the six-pulse voltages must be phase shifted by π/6. Such phase shifting can be obtained using transformers with different secondary winding connections - Y and Δ. The ac supply voltages - secondary voltage in Δ connection u _2a2 (for example)and line-to-line voltages in Y connection u _2ab1 (u _2a1 - u _2b1) must be equal.

The output dc voltage is a sum of two rectified voltages, u_d = u_{d 1} + u_{d 2}. The result is a voltage with 12 pulses for one period, which has very small ripple.

Such rectifiers are used in high power supplies for many kilowatts of power.

In many applications, rectified voltage may be insufficient to meet the load requirements. In this case, voltage-multiplier rectifiers are used. They consist of a few diode-capacitor cells. The output voltage is the sum of several capacitors' voltages.

During the positive half wave of u ₂ a capacitor C ₁ is charged via diode D ₁ to the peak voltage U _2m . During the negative half wave, a capacitor C ₂ is charged via diode D ₂ to U _2m .

A current flows from the ac source for a very small time-interval around the maximum of ac voltage. The rest of the time, the load current flows through R_L due to the capacitor discharging.

Voltage-multiplier rectifiers are used for high dc voltages and very small load currents.

Many home appliances operate using ac voltage of 110 V as well as 220 V. A voltage-doubler rectifier is used to avoid a transformer - an important advantage of the circuit shown in the figure.

When an ac voltage is 110 V, the switch is in the right position. Each capacitor charges to maximum value of the ac voltage u_{c 1} = u_{c 2} = U _1m = 155.5 V. The rectified voltage u_d doubles. It is the sum of the two capacitor voltages - U_d = 2 U _1m ≈ 311 V dc.

If an ac supply voltage is 220 V then the switch is in the left position. The circuit operates as a single-phase bridge rectifier. The rectified voltage U_d = U _1m = 220.1,414 ≈ 311 V dc.

Kinescopes and equipment for electrostatic painting require high voltages (up to 100 kV) with load current less than 1mA. A voltage-multiplier rectifier with multiplying coefficient more than 3 is used for this purpose. It is constructed using technique shown in the figure.

Initially, when ac voltage u ₂ is positive, the capacitor C ₁ charges via diode D ₁ to voltage U_{c 1}=U _2m . If a second similar diode-capacitor cell is added to the circuit, the secondary voltage source u ₂ and the voltage source U_{C 1} charge C ₂ via diode D ₂ during negative half waves. In a few periods U_{c 2} = 2U _2m . If a third cell is added the capacitor C ₃ will be charged through the secondary winding, C ₁, D ₃, C ₂. Its steady state voltage is U_{c 3} = 2U _2m . And so on.

Almost all electronic circuits require a constant dc supply voltage for proper operation. A stabilizer is not a compulsory part of a dc supply unit. It is used when a high stability of dc voltage is required.

A diode rectifier produces dc voltage consisting of a constant voltage with average value U_d and of an ac ripple component. The average value depends on variations of a line voltage. A stabilizer maintains a constant dc voltage for variations in the input voltage or in the load, making ripple negligible. The stabilizer can be considered an ideal voltage source with constant output dc voltage U_st .

The basic functional block diagram of a linear voltage stabilizer is shown in figure. It consist of a reference (circuit that produces reference voltage U_ref ), voltage divider (that gives feadback voltage U_fb ), circuit for analog comparison, an error amplifier, and output stage. The stabilized output voltage is obtained as a difference U _st = U _d - U_CE . The stabilizer keeps output voltage constant by monitoring its changes and correspondly controlling the collector-emitter voltage U_CE in a proper way. For this purpose feadback voltage U_fb , which is proportional to the U_st variations, is compared with U_ref . The difference, named error, is amplified and controls the U_CE .

Construct the linear stabilizer circuit.

If the input voltage increases, the output voltage also increases. Feedback voltage U_fb as a part of output voltage also increases. So the base voltage of the transistor T ₂ increases. At the same time U_ref is a constant. The base-emitter junction compares these two voltages. Their difference, called "error", is amplified by transistor T ₂ and its collector current increases. According to the Kirchoff's law, the base current of T ₁ decreases ( I_s from the current source is constant). Correspondingly, the voltage U_CE of the transistor T ₁ increases. This prevents the output voltage from further increasing . The current source could be replaced by a resistor.

Voltage stability can be improved by increasing the voltage gain of the error amplifier. For this purpose, an operational amplifier is used instead of transistor. Unfortunately, it produces oscillations in the output voltage. To avoid this, a capacitor is included in the circuit.

On-chip implementation yields an improvement in stabilizer parameters. The integrated stabilizers are easy to use and have a better output voltage stability, internal over current and temperature protection.

A popular series of IC stabilizers for fixed, positive, or negative voltage are 78XX and 79XX. The last two digits (XX) display the output voltage. For example 05 is for 5V, 15 is for 15V