There are three types of inverter. An inverter circuit which creates an ac voltage (and current) from a dc voltage source is called a voltage source inverter (VSI). Similarly, the current source inverter (CSI) creates an ac current (and voltage) from a dc current source. A third converter type is called a resonant inverter. The load is a series resonant circuit that produces a high frequency sine-wave ac voltage.

The dc voltage supplying the inverters is obtained from batteries or by rectifying the line voltage. Thus energy conversion sometimes takes place twice, from ac to dc then from dc to ac.

Voltage source inverters are used in ac motor drives and uninterruptible supply systems. They can be divided into two main categories.

1. Pulse-Width-Modulated (PWM) inverters. The input dc supply voltage is constant. The inverter controls the magnitude and the frequency of the ac output voltage from the inverter. The synthesized output PWM voltage simplifies filtering and obtains a pure sine-wave curve.

2. Square-wave inverters. The inverter has to control only the frequency of the output voltage. Therefore, the input dc voltage is controlled in order to control the magnitude of the ac output voltage.

Let us assume that a voltage signal is formed from the voltage sum of a set of sine waves. The first term in this sum is u₁ = U_m.sinωt. The second term is u₃ = (U_m/3).sin3ωt. The next term is u₅ = (U_m/5).sin5ωt and so on. The result is a rectangular wave.

Conversely, a rectangular wave could be described as the sum of odd sine-wave components. The most important is the wave u₁ called the first harmonic or fundamental. The other components are higher harmonics. Their number and amplitude depends on the shape of the rectangular curve.

The voltage source inverter (VSI) is supplied from a dc voltage source. A capacitor is included in parallel to the dc supply to ensure a low internal resistance for the dc source.

The output voltage is obtained by alternately closing the switch pairs S₁, S₃ and S₂, S₄. When S₁, S₃ are closed, the upper output terminal is positive with respect to the lower and vice-versa when S₂, S₄ are closed. Thus the inverter produces an ac voltage.

The output voltage formed has a rectangular (square-wave) shape. Its amplitude is equal to the supply voltage U_d. The output inverter current depends on the load.

If the dc supply source is symmetrical about "0", the voltage at point "a" - u_ao depends on switches S₁ and S₄. If S₁ is closed the voltage at "a" is + 0.5U_d. Alternatively, when S₄ is closed (S₁ is opened), the voltage at "a" is - 0.5U_d. It is not permissible to simultaneously close S₁ and S₄. S₂ and S₃ switch on and off in a similar way. The output voltage is obtained from the voltage difference u_out = u_ao - u_bo. The output voltage u_out is a square-wave with amplitude equal to U_d.

The first harmonic (fundamental) is shown in the diagram. It may be obtained by filtering the square wave voltage (the filter is not shown in the diagram).

The positive half wave of the output voltage is created when the switches S₁ and S₃ are closed. Current flows from the source +U_d through S₁, load (L and R_L) and S₃ to -U_d.

The negative half wave is formed when switches S₂ and S₄ are closed. Due to the energy stored in the inductor L_L the current through the load continues to flow in the positive direction. Thus it flows from -U_d through S₄, load and S₂ to +U_d. When the inductor's energy is dissipated, the load current falls to zero and changes the direction. Now it flows from +U_d through S₂, load (L and R_L) and S₄ to -U_d. Hence, an inductor in the load imposes a very important requirement for bi-directionally conducting switches in a VSI.

In a real VSI the switches are implemented using power semiconductor devices - old-fashioned thyristors or transistors. An anti-parallel diode is connected to the devices.

With a purely resistive load only the transistors provide power. If a load is resistive-inductive, after switching off the transistors (for example T₁ and T₃ ), the diodes D₂ and D₄ conduct. Thus the inductor feeds the stored energy back into the dc source at the beginning of the negative half period. After dissipating the stored inductor energy, T₂ and T₄ begin conducting.

The voltage across the transistors is approximately equal to the supply voltage U_d.

Three VSI circuit topologies are primarily used: bridge, half-bridge and push-pull. The first operates with four power devices, the others with two devices.

Half bridge circuits use one half of the dc supply voltage. Hence, its output voltage and power are half that of the other circuits.

Push-pull circuits allow easy driving of transistors but require a transformer and the transistor voltage is twice as high. The output voltage depends on the transformer ratio.

The bridge circuit is the most powerful circuit. The voltage across the transistors is equal to supply voltage U_d. The load could be supplied with ac via a transformer.

The VSI may be controlled in more flexible way. Two legs of the bridge (T₁, T₄ and T₂, T₃) can be driven by phase-shifted pulses. Then the voltages at points "a" and "b" have the shapes shown in the illustration.

The output voltage consists of three different states. The third, zero state, is due to simultaneously turning on the transistors T₁ and T₂ or T₃ and T₄.

The phase shift Ψ determines the zero state duration and the amplitude (rms value) of the output voltage u_out.

A three-phase VSI feeding a Y-connected load from a center-tapped dc source is shown in the illustration. It consists of three legs, each with two switches - S₁/S₄, S₃/S₆, S₅/S₂. Every leg is driven such that the next is delayed by 120°(2π/3). Each switch conducts for 180°. The voltages u_ao, u_bo and u_co are square-waves as shown.

It may be seen that during the operating period the circuit has six different states. Three switches conduct in each state. When a switch is turned on, another switch turns off. This determines a new current path and a new circuit state.

The three-phase VSI produces a three-phase voltage system with respect to the neutral point (N) of the Y connection. The output line voltages are u_A, u_B, u_C.

The line voltage u_A is positive, for example, when S₁ is closed. The voltage is 1/3U_d when two of the upper switches are closed. The voltage value is 2/3U_d if two lower switches are closed. The voltage u_A is negative when S₄ is closed. The voltage value is (-1/3U_d ) when two of the lower switches are closed and (-2/3U_d ) if two upper switches are closed.

The line voltages u_B and u_C are identical but phase-shifted by 120°.

A three-phase VSI with Δ connected load is shown in the illustration. The switches operate in the same manner as with a Y-connected load. Three switches conduct during every time interval. The voltages u_ao, u_bo and u_co have the same square-wave shape.

Line-to line voltage u_ab is given by the difference u_ab = u_ao - u_bo.

The line-to-line voltages u_bc and u_ca are identical but phase shifted by 120°. Their first harmonics are pure sine waves and are shown in the illustration.

Let us assume two ac voltage sources u₁ and u₂ are connected in series. The voltage source u₂ is phase shifted by an angle Ψ. The load voltage is the sum of both voltages - u_L = u₁ + u₂ = U_m.sinωt + U_m.sin(ωt + Ψ). Such a sum is known as a scalar sum. If the angle Ψ = 0, the load voltage is at its maximum value. When the angle Ψ = 180° (π), the load voltage drops to zero. Note that voltage u₁ and u₂ have unchanged amplitude U_m during this regulating operation.

Therefore, the load voltage may be regulated from zero to a maximum value depending on the phase-shift angle Ψ.

Two ac voltage sources u₁ and u₂ connected in series may be implemented using two VSIs. The control circuit must produce gate pulses in such a way as to phase-shift the voltage u₂.

It is only possible to sum voltages if the VSI outputs are electrically isolated. The sum is obtained using different dc voltage sources or incorporating the output transformers in the VSI.

The load voltage is the sum of both output VSI voltages, electrically isolated. It is a square-wave. The load voltage is regulated from zero to its maximum by changing the angle Ψ.

The voltage produced from a VSI has a rectangular form. However, a lot of practical applications need a sinusoidal voltage shape. A VSI can easily produce a sine-wave form based on a sequence of square wave pulses. For this purpose a low frequency sine-wave signal called a modulated signal is sliced into short time intervals. Their duration is T_s, which is called the carrier period. At the mid-point of any time interval T_s a square wave pulse is input, the width of which is modulated in accordance with the value of the low frequency sine-wave as shown in the illustration.

The method described is known as Pulse Width Modulation (PWM).

The value of output voltage is determined by the modulation ratio μ.

The amplitude of an output voltage depends on the modulation ratio μ and the supply voltage U_d. It is less than U_d. Using PWM allows the rms value of the output voltage to be changed by varying the modulation ratio. Therefore, a VSI can operate with constant supply voltage, which simplifies the power circuit.

Usually the ratio of carrier frequency to modulating frequency f_s/F is not changeable and is very high. The synthesized pulse sequence consists of a fundamental harmonic and high frequency harmonics. The lowest high frequency harmonic occurs with carrier frequency f_s and is easily filtered.

To control the flow rate of a water pump a valve may be used. The ac motor and pump operate at maximum power and energy consumption.

A PWM VSI can control both the frequency and the amplitude of the output voltage. It is used as such in adjustable speed ac motor drives. The main requirement for such ac speed motor control is keeping the voltage/frequency ratio constant.

Using variable speed ac drives conserves energy significantly.

The current source inverter (CSI) requires that the dc supply system functions like a dc current source. This is implemented by placing a large inductor L in series with the dc system.

The positive half wave of the ac output current is formed when the thyristors Th₁ and Th₃ turn on. The current flows through +U_d, L_d, Th₁, C_L - R_L, Th₃, -U_d. When Th₂ and Th₄ are conducting, the negative half-wave is formed. A square-wave ac current i_L is created that passes through a parallel load circuit C_L - R_L. This capacitance makes the load voltage lag behind the square-wave current. The shape and amplitude of the load voltage depends on variations in C_L (or R_L).

The switches in a CSI are mostly implemented using thyristors. To guarantee that the thyristor can turn off, a capacitive load impedance is required. The simplest load consists of a load resistor R_L and an auxiliary capacitor C_L.

At the end of a half-period when Th₁ and Th₃ are conducting, the capacitor voltage has the polarity shown in the illustration. When Th₂ and Th₄ turn on, Th₁ and Th₃ are switched off by the capacitor voltage. When Th₂ is on, it connects the capacitor C_L to Th₁ and reverse biases it. Th₂ turns off reliably if the time t ^- that the thyristor voltage is negative is long enough - t ^-=t_q.

The thyristor current is a square wave with high di /dt, which is one disadvantage of a CSI.

The main disadvantage of a CSI is the large variation in load (and thyristor) voltage when the load is changed. The load parameters (R_L, C_L, frequency) have an equal influence over the operation of the inverter. The load (thyristor) voltage may rise by a factor of 5 due to a variation in load. The load variations have an effect on the time t ^- when the thyristor voltage is negative.

To avoid this disadvantage of CSIs, a modified CSI circuit with additional series diodes is used as shown in the diagram. This modified CSI is used in ac power drives (especially in a three-phase implementation).

A three-phase CSI with Δ connected load is shown in the illustration. A three-phase voltage and current system is formed when the appropriate thyristor turns on. At any time only two thyristors conduct simultaneously. The current flow in the circuit for every single operating stage can be seen in the diagram.

The load capacitors make the load voltage lag behind the square-wave current. They provide the negative voltage for thyristor commutation.

In a parallel RLC circuit the currents in the inductive I_L and the capacitive I_C branches are always 180° out of phase with one another and the current I_CL = | I_L - I_C |.

In such a parallel RLC circuit parallel resonance occurs when the inductive reactance X_L equals the capacitive reactance X_C. For a given RLC circuit this happens at only one specific frequency called the resonant frequency f_r. When X_L = X_C the two branch currents are equal in magnitude. Thus the current I_CL is zero and the impedance of the parallel LC circuit is infinitely large. The total impedance reaches a maximum at the resonant frequency f_r and decreases above and below f_r.

In the voltage and current source inverters the inverter switches operate in switched mode. The switches are objected to high switching stresses and high switching power loss.

These shortcomings are removed when the voltage across the switches or the current through them is zero at the switching instant. This requires changes in converter topology. The load is an LC series resonant circuit so that these inverters are classified as resonant inverters . Another significant result is the reduction in electro-magnetic influence (EMI). For proper operation resonant inverters require a dc voltage source. Widespread applications include induction heating and dc-to-dc converters.

Resonance in an electrical circuit acts as the basis for frequency tuning. In series RLC circuits inductor voltage U_L and capacitor voltage U_C effectively subtract because they are always 180° out of phase with each other as illustrated by the waveforms.

In a series RLC circuit series resonance occurs when the inductive reactance X_L equals the capacitive reactance X_C. For a given RLC circuit this only happens at one specific frequency called the resonant frequency f_r. Since X_L = X_C the reactances effectively cancel out and the total impedance Z is purely resistive. The total impedance is a minimum at resonance frequency f_r, but increases above and below f_r.

The most popular thyristor bridge circuit is shown in the diagram.

The first (positive) half-wave of the ac output voltage is formed when thyristors Th₁ and Th₃ turn on. The current flows through +U_d, L_o1, Th₁, L_o2, C_o, R_L, Th₃, -U_d. It has a sinusoidal form, rises to its maximum value I_m and falls to zero. This causes the thyristors to turn off. No current flows and no changes occur in the circuit until the thyristor pair Th₂ and Th₄ switch on. Then the current flows through the load in the opposite direction. The negative half-period of the load voltage is generated. An ac output voltage is produced from a dc supply.

Due to the resonance, the capacitor voltage U_Cmax is greater than the supply voltage U_d.

An important feature of resonant inverters is self-commutation; once the thyristor is turned on, it initiates a process which causes the thyristor to turn off. The anode-cathode thyristor voltage at the end of every half-period is defined by the difference (U_d - U_Cmax). Because the capacitor voltage U_Cmax > U_d, the thyristor voltage is negative and causes it to turn off. The time t ^-, when the thyristor voltage is negative, must be enough to ensure that the thyristor turns off reliably (t =t_q).

The current through the thyristor has a sinusoidal form.

The circuit is shown in the diagram. Its mode of operation depends on the relation between the switching frequency f_s (respective period T_s ) and the series resonant frequency f_o (T_o).

If T_s > 2T_o and T₁, T₃ are on, the load current flows through +U_d, T₁, L_o, C_o, R_L, T₃, -U_d. It has a sinusoidal form, reaches maximum and falls to zero.

At zero current the capacitor voltage reaches its maximum value, higher than the supply voltage. This creates the opportunity for current to flow in the opposite direction from the capacitor's positive terminal through L_o, D₁, U_d, D₁, R_L, to the capacitor's negative terminal. T₂ and T₄ operate in the same manner.

When T_o < T_s < 2T_o and T₁, T₃ are on, the load current flows through +U_d, T₁, L_o, C_o, R_L, T₃, -U_d. It reaches maximum and falls to zero. Then current flows in the opposite direction - through C_o, L_o, D₁, U_d, D₃, R_L.

At a certain instant the transistors T₂ and T₄ turn on. This occurs when the load current is non-zero. Hence, conditions when switching on the transistor are undesirable: voltage is high (U_d ) and current is non-zero. When switching off the transistor, conditions are ideal - current and voltage are both zero. Switching the transistor at zero current is known as ZCS (zero current switching). Similarly ZVS means zero voltage switching.

When the transistors T₁ and T₃ switch on, the current flows through +U_d, T₁, L_o, C_o, R_L, T₃, -U_d. The transistors turn off before the natural end of the resonant half-wave. Because of the energy stored in series inductance L_s, the current continues to flow in the same direction through -U_d, D₄, L_o, C_o, R_L, D₂, +U_d.

Hence, conditions for switching on the transistor are ideal - current and voltage are both zero. Conditions for switching off the transistor are not ideal: voltage is high (U_d ) and current is non-zero. The main advantage of transistor resonant inverters is that the voltage across the transistors changes between 0 V and U_d. It is not dependent on the Q-factor of the resonant circuit.

Since transistor switching losses in resonant inverters are very small, they are used in high and very high frequency applications involving frequencies of tens or hundreds of kilohertz.

A typical application is the use of resonant inverters in dc-to-dc converters. The circuit is shown in the diagram. The rectifier included in the inverter circuit rectifies the high frequency ac resonant current. Thus, the load current is a sequence of positive sinusoidal half-waves with very high frequency. This reduces the need for filtering and makes it very easy to produce an almost pure dc voltage.