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Working principle of half wave controlled converter

Working principle of half wave controlled converter

 

Let us consider the circuit in Figure (a) with a resistive load.

working principle of half wave controlled converter

During the positive half-cycle of input voltage, the thyristor anode is positive with respect to its cathode, and the thyristor is said to be forward-biased. When thyristor T1 is fired at ωt = α, thyristor T1 conducts and the input voltage appears across the load.

ইনপুট ভোল্টেজের পজিটিভ অর্ধ-চক্রের সময়, থাইরিস্টরের অ্যানোড তার ক্যাথোড থেকে বেশি পজিটিভ হয়, এবং থাইরিস্টরকে বলা হয় ফরোয়ার্ড-বায়াসড। যখন থাইরিস্টর T1কে ωt = α অ্যাঙ্গেল এ ফায়ার করা হয়,তখন থাইরিস্টর T1 সঞ্চালন করে এবং ইনপুট ভোল্টেজ লোড জুড়ে প্রদর্শিত হয়।

When the input voltage starts to be negative at ωt = π, the thyristor anode is negative with respect to its cathode, and thyristor T1 is said to be reverse-biased; and it is turned off. Figure (b) shows the waveforms of input voltage and output voltage.

যখন ইনপুট ভোল্টেজ ωt = π এ ঋণাত্মক হতে শুরু করে, তখন  থাইরিস্টরের অ্যানোড তার ক্যাথোডের থেকে ঋণাত্মক হয় এবং থাইরিস্টর T1 কে বিপরীত-পক্ষপাতী বলা হয়; এবং এটি বন্ধ হয়। চিত্র (b)তে ইনপুট ভোল্টেজ এবং আউটপুট ভোল্টেজের তরঙ্গরূপ দেখানো হয়েছে।

\begin{array}{l}If\;V_m\;is\;the\;peak\;input\;voltage,\;the\;average\;output\;voltage\;V_{dc}\;can\;be\;found\;from\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;V_{dc}=\frac1{2\mathrm\pi}\int_\alpha^{\mathrm\pi}V_m\sin\omega td(\omega t)\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{V_m}{2\mathrm\pi}\lbrack-\cos\omega t\rbrack_\alpha^{\mathrm\pi}\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{V_m}{2\mathrm\pi}(1+\cos\omega t)\;\end{array}

 

and Vdc can be varied from Vm /π to 0 by varying α from 0 to π. The average output voltage becomes maximum when α=0 and

The maximum output voltage Vdm is

{\boldsymbol V}_{\mathbf d\mathbf m}\boldsymbol=\frac{{\mathbf V}_{\mathbf m}}{\mathbf\pi}

The root-mean-square(rms) output voltage is given by

\begin{array}{l}\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\boldsymbol V}_{\mathbf r\mathbf m\mathbf s}\boldsymbol=\boldsymbol\lbrack\frac{\mathbf1}{\mathbf2\mathbf\pi}\boldsymbol\int_{\mathbf\alpha}^{\mathbf\pi}\boldsymbol V_{\mathbf m}^{\mathbf2}\boldsymbol\;\mathbf{sin}^{\mathbf2}\boldsymbol\omega\boldsymbol t\boldsymbol\;\boldsymbol d\boldsymbol(\boldsymbol\omega\boldsymbol t\boldsymbol)\boldsymbol\rbrack^\frac{\mathbf1}{\mathbf2}\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\boldsymbol=\boldsymbol\lbrack\frac{\mathbf V_{\mathbf m}^{\mathbf2}}{\mathbf4\mathbf\pi}\boldsymbol\int_{\mathbf\alpha}^{\mathbf\pi\boldsymbol+\mathbf\alpha}\boldsymbol\;\boldsymbol(\mathbf1\boldsymbol-\mathbf{cos}\mathbf2\boldsymbol\omega\boldsymbol t\boldsymbol)\boldsymbol\;\boldsymbol d\boldsymbol(\boldsymbol\omega\boldsymbol t\boldsymbol)\boldsymbol\rbrack^\frac{\mathbf1}{\mathbf2}\\\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{{\mathbf V}_{\mathbf m}}{\mathbf2}\boldsymbol\lbrack\frac{\mathbf1}{\mathbf\pi}\boldsymbol(\mathbf\pi\boldsymbol-\mathbf\alpha\boldsymbol+\frac{\mathbf{sin}\mathbf2\mathbf\pi}{\mathbf2}\boldsymbol)\boldsymbol\rbrack^\frac{\mathbf1}{\mathbf2}\end{array}

Working principle of half wave controlled converter

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