1. Switch-Mode DC-AC Inverters
Applications:
ac motor drives
Uninterruptible ac power supplies
Where a sinusoidal ac output is required whose magnitude and frequency both have to be controlled
Terminal voltage is adjustable
in its magnitude and frequency

2. Switch-Mode DC-AC Inverter: Bi-directional power flow

3. Switch-Mode DC-AC Inverter: Basic concepts
Inverters with single- and three-phase ac outputs will be discussed
Input is dc voltage source
Such inverters are called voltage-source inverters (VSI)
The other type of inverter is a current-source inverter (CSI) where the input is a dc current source
Discussion will be limited to VSI
Four-quadrant operation
Rectifier mode: quadrants 2 and 4
Inverter mode: quadrants 1 and 3

4. Switch-Mode DC-AC Inverter: Basic concepts (cont’d)
vo can be assumed to be sinusoidal
io will lag vo since the inverter will drive an inductive load such as a motor
In interval 1, both vo and io are positive and interval 3, both vo and io are negative
Therefore during intervals, 1 and 3, po=voio will be positive, and power will flow from the dc to ac side which is the inverter mode of operation
During the intervals 2 and 4, vo and io will be opposite signs, and power will flow from the ac side to the dc side which is the rectifier mode of operation
Thus, switch-mode inverters are capable of operating in all four quadrants

5. Frequency modulation ratio, mf=fs/f1
Synthesis of a Sinusoidal Output by PWM
One-leg inverter
Inverter output to be sinusoidal with voltage and frequency controllable
Inverter switching frequency is determined by
- Sinusoidal control signal – which is used to modulate the switch duty ratio and has a frequency f1.
- Triangular waveform
Output voltage magnitude fluctuates between Vd /2 and –Vd /2
Output voltage frequency is determined by the control signal frequency
Vd/2
-Vd/2
Frequency modulation ratio, mf=fs/f1

6. Single Phase Half-Bridge Inverter
Two equal capacitors are connected in series across the dc input
Vd /2 is the voltage across each capacitor
Items of importance:
- peak amplitude of the fundamental frequency component Vo1 is
ma (=Vcontrol /Vtri) times Vd /2
- harmonics in the inverter output voltage waveforms

7. Single Phase Half-Bridge Inverter (cont’d)
The switches T+ and T- are controlled based on the comparison of vcontrol and vtri
When vcontrol > vtri , T+ is on and vAo=Vd /2
When vcontrol < vtri , T- is on and vAo=-Vd /2
Since the two switches are never off simultaneously, the output voltage vAo fluctuates between Vd /2 and -Vd /2.

8. Harmonic Spectrum of VAo
The normalized harmonic voltages with significant amplitudes are plotted
This plot shows three items of importance:
The peak value of the fundamental frequency component is ma times Vd/2.
Harmonics appear as side bands, cantered around the switching frequency
The harmonic mf should be an odd integer.

9. Fundamental Frequency Component of VAo
The peak amplitude of the fundamental-frequency component (VAo)1 is ma times Vd/2. This can be explained by first considering a constant vcontrol as shown in the following figure.
The average output voltage (or more specifically, the output voltage averaged over one switching time period Ts = 1/fs) VAo depends on the ratio of Vcontrol to Vtri for a given Vd

10. Fundamental Frequency Component of VAo (Cont’d)
Let us assume that Vcontrol varies very little during a switching time period, that is, mf is large.
Therefore, assuming Vcontrol to be constant over a switching time period, following figure indicates how the "instantaneous average" value of vAo (averaged over one switching time period Ts) varies from one switching time period to the next. This "instantaneous average" is the same as the fundamental-frequency component of vAo.

11. Fundamental Frequency Component of VAo (Cont’d)
The average output voltage (or more specifically, the output voltage averaged over one switching time period Ts = 1/fs) VAo depends on the ratio of Vcontrol to Vtri for a given Vd
which shows that in a sinusoidal PWM, the amplitude of the fundamental-frequency component of the output voltage varies linearly with ma. Therefore, the range of ma from 0 to 1 is the linear range.

12. Harmonics in the Inverter Output Voltage VAo
The harmonics in the inverter output voltage waveform appear as sidebands, centered around the switching frequency and its multiples, that is, around harmonics mf, 2mf, 3mf, and so on. This general pattern holds true for all values of ma in the range 0-1.
the harmonic amplitudes are almost independent of mf, though mf defines the frequencies at which they occur. Theoretically, the frequencies at which voltage harmonics occur can be indicated as
fh = (jmf ± k)f1
that is, the harmonic order h corresponds to the kth sideband of j times the frequecy modulation ratio mf.
h = j(mf) ± k
where the fundamental frequency corresponds to h = 1. For odd values of j, the harmonics exist only for even values of k. For even values of j, the harmonics exist only for odd values of k.

13. Harmonics in the Inverter Output Voltage VAo

14. Single-Phase Full-Bridge Inverter
Consists of two one-leg inverters
Preferred over other arrangements in higher power ratings
With the same dc input voltage, output voltage is twice that of the half-bridge inverter

15. PWM to Synthesize Sinusoidal Output
When TA+ is ON, vAo=Vd/2
When TB- is ON, vBo= - Vd/2
vBo(t)= - vAo(t)
vo(t)= vAo(t) - vBo(t) = 2 vAo(t)
Peak of the fundamental frequency component:
where the amplitude modulation ratio
Output voltage switches between Vd and - Vd

16. Example 1: Switch-mode inverter (one phase-leg, half bridge)
A general analysis of the switch-mode inverter (shown in the figure below) is to be done. The switching frequency fs, which is also the frequency of the triangular signal is 1450 Hz. The DC voltage, Vd, is 600 V. Output voltage is sinusoidal voltage with a frequency equal to 50 Hz. The load is connected between the inverter leg A and the dc voltage midpoint o. Vd
Vd / 2
TA+
TA-
DA+
DA- io A N + -
vAN o
Find the frequency modulation ratio, mf.
Calculate the output voltage (rms value of 1. harmonic), when the amplitude modulation ratio, ma, is equal to 0.8?
Prove that (Vo1)peak = ma (Vd / 2 ).
Compute the rms value of the 5 most dominant harmonics of vAo (at ma=0,8), by using Table 8-1, page 207. Also indicate the frequencies at which these harmonics appear.

17. Example 2: Bipolar single phase half bridge inverter

18. Single-Phase Push-Pull Inverters
requires a transformer with a center-tapped primary
T1 is ON (and T2 is OFF):
vo=Vd/n, where n is the transformer turns ratio.
T2 is ON (and T1 is OFF):
vo= - Vd/n
The peak value of the fundamental component of the output voltage:
Vo1= ma (Vd/n)

19. No more than one switch in series conducts at any instant of time
Less switching voltage drops
Thus, this results in a significant improvement in energy efficiency

20. Three-Phase Inverter Used to supply three-phase loads
Three single-phase inverters could be used, however, 12 switches are necessary, as a result, less efficient
Consists of three legs, one for each phase
One of the two switches in a leg is always ON at any instant
Output of each leg depends on Vd and the switching status

22. Summary dc-to-ac converters are known as inverters
The function of an inverter is to change the dc input voltage to an ac output voltage of desired magnitude and frequency
The output voltage waveforms of ideal inverters should be sinusoidal
However, the output of practical inverters contains harmonics
For high power applications, low distorted sinusoidal waveforms are required
Harmonic contents could be minimized by the use of high-speed semiconductor switching techniques
Inverters are widely used in industrial applications
- motor drives, UPS, induction heating, standby power supplies, etc.
- input may be a battery, fuel cell, solar cell, or there dc source
dc-to-ac inverters can make smooth transition into the rectification mode, where the flow of power reverses from the ac side to the dc side
Two types of inverters: single-phase inverters and three-phase inverters