A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across 'ab' as shown. To achieve a modulation index of 0.8, the angle \theta expressed in degrees should be ___________ (Round off to 2 decimal places.) (Modulation index is defined as the ratio of the peak of the fundamental component of {V}_{ {ab}} to the applied {DC} value.)

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A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across 'ab' as shown. To achieve a modulation index of

0.8

, the angle

θ

expressed in degrees should be ___________ (Round off to 2 decimal places.) (Modulation index is defined as the ratio of the peak of the fundamental component of

{V}_{ {ab}}

to the applied

{DC}

value.)

Your Answer:

Validate

Solution:

Supply voltage

=325 {V}

Amplitude of fundamental component of output voltage can be expressed as:

{V}_{01}= {m}_{ {A}} × {V}_{ {s}}=0.8 × 325=260 {V}

....(1)

From the given waveform,

Pulse width of output voltage,

2 {d}=π-φ ⇒ {d}=\;{π}/{2}-φ

Fourier series expansion of square wave will be:

V_{0}=∑↙{n=1,3,5}↖{∞} \;{4 V_{s}}/{n π} \sin n d \sin n ω t

Fundamental voltage,

V_{01}=\;{4 V_{s}}/{π}\sin\;d

V_{01}=\;{4 V_{s}}/{n π} \sin (\;{π}/{2}-θ)=\;{4 V_{s}}/{π} \cos θ

.....(2)

Equating equation (1) and (2),

\;{4 × 325}/{π} \cos θ=260 ⇒ \cos θ=0.628

θ=51.073^{∘}

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