In a transistor Colpitt's oscillator L = 100uH, C = 0.6uF, C1 = 0.001uF and C2 = 0.01uF. Calculate

To calculate the characteristics of a Colpitt's oscillator with the given values, we need to determine the resonant frequency of the LC circuit, which is the frequency at which the oscillator will operate. The Colpitt's oscillator uses a combination of an inductor (L) and two capacitors (C1 and C2) to create a resonant tank circuit.

The resonant frequency (f) of a Colpitt's oscillator is given by the formula:

[ f = \frac{1}{2\pi\sqrt{L \cdot C_{eq}}} ]

where ( C_{eq} ) is the equivalent capacitance of the two capacitors C1 and C2 when connected in series. The equivalent capacitance of two capacitors in series is given by:

[ \frac{1}{C_{eq}} = \frac{1}{C1} + \frac{1}{C2} ]

Let's calculate ( C_{eq} ) first:

[ \frac{1}{C_{eq}} = \frac{1}{C1} + \frac{1}{C2} ] [ \frac{1}{C_{eq}} = \frac{1}{0.001\mu F} + \frac{1}{0.01\mu F} ] [ \frac{1}{C_{eq}} = \frac{1}{0.001 \times 10^{-6} F} + \frac{1}{0.01 \times 10^{-6} F} ] [ \frac{1}{C_{eq}} = 1000 + 100 ] [ \frac{1}{C_{eq}} = 1100 ] [ C_{eq} = \frac{1}{1100} \mu F ] [ C_{eq} = 0.909 \times 10^{-3} \mu F ]

Now we can calculate the resonant frequency (f):

[ f = \frac{1}{2\pi\sqrt{L \cdot C_{eq}}} ] [ f = \frac{1}{2\pi\sqrt{100 \times 10^{-6} H \cdot 0.909 \times 10^{-3} \mu F}} ] [ f = \frac{1}{2\pi\sqrt{90.9 \times 10^{-9}}} ] [ f = \frac{1}{2\pi\sqrt{90.9 \times 10^{-9} F \cdot H}} ] [ f = \frac{1}{2\pi\sqrt{90.9 \times 10^{-9} F \cdot H}} ] [ f = \frac{1}{6.2832\sqrt{90.9 \times 10^{-9}}} ] [ f \approx \frac{1}{6.2832 \times 9.53 \times 10^{-5}} ] [ f \approx \frac{1}{0.000598} ] [ f \approx 1.67 \times 10^3 Hz ] [ f \approx 1.67 kHz ]

So, the resonant frequency of the Colpitt's oscillator with the given values is approximately 1.67 kHz.