If T is the time period for a chopper circuit and δ is its duty cycle, then the chopping frequency is
A
Ton/δ
B
Toff/δ
C
δ/Toff
D
δ/Ton

Question

If T is the time period for a chopper circuit and δ is its duty cycle, then the chopping frequency is

Examoogle · Accepted Answer

δ/Ton Explanation: The chopping frequency $f$ of a chopper is defined as the reciprocal of the total time period $T$. Given the duty cycle $\delta = \frac{T_{on}}{T}$, we can derive the expression for frequency by substituting $T = \frac{T_{on}}{\delta}$. Working Principle: A chopper circuit periodically switches the input voltage to the load. The total time period $T$ is the sum of the on-time ($T_{on}$) and off-time ($T_{off}$). The ratio of $T_{on}$ to the total period $T$ determines the duty cycle $\delta$. Consequently, frequency $f = \frac{1}{T} = \frac{1}{T_{on} / \delta} = \frac{\delta}{T_{on}}$. Key Formulas: $T = T_{on} + T_{off}$ — Total time period; $\delta = \frac{T_{on}}{T}$ — Duty cycle definition; $f = \frac{1}{T} = \frac{\delta}{T_{on}}$ — Frequency calculation Key Points: Duty cycle ($\delta$) is the ratio of 'on' time to total period.; Frequency is the inverse of the time period ($T$).; The units of frequency are Hertz (Hz) or cycles per second. Advantages: Allows efficient control of DC power; High switching frequency reduces size of passive components Disadvantages: High switching losses at very high frequencies; Electromagnetic interference (EMI) issues Applications: DC motor speed control; Switch-mode power supplies (SMPS) Additional Info: The parameter $T_{on}$ represents the duration the semiconductor switch (like MOSFET or IGBT) conducts.. Option A is incorrect because $T_{on}/\delta$ equals the total period $T$, which is the inverse of frequency.. Option B is incorrect because $T_{off}/\delta$ does not represent the frequency. Answer: D is correct — The chopping frequency $f$ is given by the ratio of duty cycle $\delta$ to the on-time $T_{on}$. Exam Tip: In DC-DC converters, remember that $f = \frac{1}{T} = \frac{1}{T_{on} + T_{off}}$. Always ensure units for time are in seconds when calculating frequency in Hertz.

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