Question

A DC-to-AC series resonant converter is shown in Fig. 1. The input voltage is V de = 100V. The inductor value is L = 0.8H, the capacitor is C=0.734uF and the load resistor value is Ro = 300Ohms. The duty cycle is 50% (1) Draw the waveforms of V; and Io for relative frequency of 0.9. (2) Draw the waveforms of V; and Io for relative frequency of 1. (3) Draw the waveforms of V; and Io for relative frequency of 1.2. (4) Draw the gain (Vorms/Vin) versus frequency curves for R= 300 and R= 1500 in single graph and calculate the value of associated with each R. Q1 03 -V + V In Q2 04 Fig. 1: AC-DC series resonant converter.

Answer 1

To draw the waveforms of V and Io for different relative frequencies in a DC-to-AC series resonant converter, the resonant frequency and gain need to be calculated. The waveforms can be obtained by applying the given duty cycle and relative frequency to the converter circuit. The gain can be determined by calculating the gain for different frequencies using the given values.

Step-by-step explanation:

In order to draw the waveforms of V and Io for different relative frequencies, we need to first calculate the resonant frequency of the series resonant converter. The resonant frequency (fr) is given by:

fr = 1 / (2π√(LC))

Using the given values of L = 0.8H and C = 0.734uF, we can calculate the resonant frequency.

fr = 1 / (2π√(0.8 * 0.734 * 10^-6)) = 2.19kHz

(1) Waveforms for a relative frequency of 0.9:

When the relative frequency (f / fr) is 0.9, the input frequency (f) can be calculated as:

f = 0.9 * fr = 0.9 * 2.19kHz = 1.971kHz

The waveforms of V and Io can be obtained by applying the given duty cycle (D = 50%) and relative frequency (f / fr = 0.9) to the converter circuit. However, since the circuit diagram is not provided, it is not possible to draw the exact waveforms.

(2) Waveforms for a relative frequency of 1:

When the relative frequency is 1, the input frequency is equal to the resonant frequency (f = fr = 2.19kHz). Using the given duty cycle (D = 50%), the waveforms of V and Io can be determined by applying the duty cycle to the converter circuit.

(3) Waveforms for a relative frequency of 1.2:

When the relative frequency (f / fr) is 1.2, the input frequency (f) can be calculated as:

f = 1.2 * fr = 1.2 * 2.19kHz = 2.628kHz

Using the given duty cycle (D = 50%), the waveforms of V and Io can be obtained by applying the duty cycle to the converter circuit.

(4) Gain versus frequency curves for R = 300 and R = 1500:

To draw the gain (Vorms / Vin) versus frequency curves for R = 300 and R = 1500, we need to calculate the gain for different frequencies.

The gain is given by:

Gain = Vorms / Vin = (1 / √((1 - D)^2 + (2πfrCR)^2))

Using the given values of D = 50%, fr = 2.19kHz, C = 0.734uF, and R = 300 or R = 1500, we can calculate the gain for different frequencies and plot the curves on a graph.

Associated values of f can be obtained by multiplying fr with relative frequency.

Value of fr for R = 300:

fr = 1 / (2π√(0.8 * 0.734 * 10^-6)) = 2.19kHz

Value of fr for R = 1500:

fr = 1 / (2π√(0.8 * 0.734 * 10^-6)) = 2.19kHz