This document discusses single phase inverters. It describes: 1. Single pulse width modulation, which controls output voltage by varying the width of pulses in each half cycle compared to a triangular carrier signal. 2. A single phase half bridge inverter, which uses two switches and capacitors to divide the DC source voltage. Feedback diodes provide current continuity for inductive loads. 3. A full bridge single phase inverter, which uses four thyristors controlled such that only one pair conducts at a time to produce an AC output voltage from the DC source. Feedback diodes allow current to flow when thyristors turn off.

1. Single Phase Inverter
1.1 Introduction
An inverter is a DC to AC converter that converts a DC voltage into an AC of
variable voltage and variable frequency. They are also referred as Voltage
Source Inverters. In inverter circuits power semi conductor devices such as
thyristors, MOSFETs, IGBTs, BJTs and GTOs can be used. If a thyristor is used,
forced commutation circuits are required to turn it OFF. A MOSFET and IGBT are
fully controlled devices. If they are used, a very high switching frequency can be
implemented.
1.2 Pulse-width modulation (PWM)
It is a technique used to control the power supplied to electrical devices,
especially to loads. The average value of voltage fed to the load is controlled by
turning the switch on and off at a fast rate.The longer the switch is on the higher
the total power supplied to the load. The PWM switching frequency has to be
much higher so the resultant waveform must be as smooth as possible. The
frequencies at which the power supply must switch depend on load and
application. The term duty cycle describes the proportion of 'on' time to the
regular interval or 'period' of time.
𝑡𝑜𝑛 = 𝐷𝑇𝑠
Where D is the duty cycle,
Ts is the total period
ton is the a time for which the switch is ON.
A low duty cycle corresponds to low power, because the power is off for most of
the time. Duty cycle is expressed in percent, 100% being fully on.
The main advantage of PWM is that power loss in the switching devices is very
low. When a switch is off there is practically no current, and when it is on and
power is being transferred to the load, there is almost no voltage drop across the
switch. Power loss, being the product of voltage and current, is thus in both
cases close to zero. PWM also works well with digital controls, which, because of
their ON/OFF nature, can easily set the needed duty cycle.

2. Here we discuss some techniques of pulse width modulation.
1.2.1 Single Pulse Width Modulation
In single pulse width modulation control, there is only one pulse per half cycle
and the output rms voltage is changed by varying the width of the pulse. The
gating signals are generated by comparing the rectangular control signal of
amplitude with triangular carrier signal. The frequency of the control signal
determines the fundamental frequency of output voltage.
1.3 Single Phase Half Bridge Inverter
1.3.1 Introduction
It is known as basic building blocks for full bridge, three phase inverters. There
are 2 switches, dividing the dc source voltage into two parts with the capacitors.
Each capacitor has the same value and has voltage Vdc / 2. The top (S1) and
bottom (S2) switch must be complementary to each other. When S1 is closed, S2
must be opened and vice versa. Feedback (freewheeling) diodes are required to
provide continuity of current for inductive loads but for resistive loads they have
no role. It provides current to flow even switches are opened. Using a diode in
parallel with a unidirectional device is common practice. Should the device be
subjected to a reverse-polarity voltage, a dangerous situation might occur. If the
voltage is high enough, an electric arc might destroy the device. With a diode,
however, applying a reverse voltage will result in current owing through the
diode. This may only destroy the diode, which can be easily and inexpensively
replaced.

3. For Resistive load
As our output is square wave it is also known as square wave inverter.
For inductive load
1.4 Full Bridge single phase inverter
1.4.1 Introduction
Single phase full bridge inverter consists of four SCRs and four diodes. For Full
bridge inverter when T1, T2 conduct, load voltage is Vs and T3, T4 conduct load
voltage is –Vs. Frequency of output voltage can be controlled by varying the
periodic time T. During inverter operation it should be ensured that two thyristors
in the same branch should not conduct simultaneously as this would lead to a
direct short circuit of the source. For inductive load, load voltage and load current

4. will not be in phase with each other. In this case diodes D1, D2, D3 and D4
connected in anti-parallel will thyristors will allow the current to flow when main
thyristors are turned off. As the energy is fed back to the dc source when these
diodes conduct, these are called feedback diodes. Operation of series R-L-C
load can be explained for R-L-C under damped and over damped load. R-L-C
Over Damped Load: Before t = 0, thyristors T3 and T4 are conducting and load
current i0 is flowing from B to A, i.e. in reverse direction. This current is at t =0.
After T3 and T4 are turned off at t = 0, current cannot change its direction
immediately because if the nature of load. As a result diodes D1 and D2 starts
conducting after t = 0 and allow i0 to flow against the supply voltage Vs. A soon
as D1 and D2 begin to conduct, the load is subjected to Vs. Though T1 and T2
are gated at t = 0, these SCRs will not turn on as these are reverse biased by the
voltage drop across the diodes D1 and D2. When Load current through D1 and
D2 falls to zero, T1 and T2 becomes forward biased by source voltage Vs. Now
T1 and T2 get turned on as these are gated for the period of T/2 seconds. Now
load current flows in the positive direction from A to B. At t = T/2; T1 and T2 are
turned off by forced commutation and as load current cannot reverse
immediately, diodes D3 and D4 come into conduction to allow the flow of current
i0 after T/2. Thyristor T3 and T4 though gated will not turn on as these are
reverse biased by the voltage drop in diodes D3 and D4. When the current in
diodes D3 and D4 drops to zero; T3 and T4 are turned on as these are already
gated R-L-C Over Damped Load: For R-L-C under damped load after t = 0,
thyristor T1 and T2 are carrying load current . As i0 through T1 and T2 reduces
to zero at t1, these SCRs are turned off before T3 and T4 are gated. As T1 and
T2 stops conducting, current through the load reverses and now is carried by
diodes D1 and D2 as T3 and T4 are not yet gated. The diodes D1 and D2 are
connected in anti-parallel to T1 and T2; the voltage drop in these diodes appears
as a reverse bias across T1 and T2. If the duration of reverse bias is more than
the SCR turn off time; T1 and T2 will get commutated naturally and therefore no
commutation circuitry is needed. This method of commutation is known as load
commutation.

5. For Resistive load
For inductive load