A Gunn diode oscillator operates at 10 GHz in a resonant eavity of 2 cm length
with a bias voltage of 6 V . The diode’s negative resistance is , and the circuit
requires a minimum power output of 50 mW .
Design the oscillator by calculating:
i) The required current for oscillation.
ii) The resonant frequency of the cavity.

Question

A Gunn diode oscillator operates at 10 GHz in a resonant eavity of 2 cm length
with a bias voltage of 6 V . The diode’s negative resistance is

, and the circuit
requires a minimum power output of 50 mW .
Design the oscillator by calculating:
i) The required current for oscillation.
ii) The resonant frequency of the cavity.

UpStudy AI · Accepted Answer

To find the required current for oscillation, we can use the formula for the power output $$ P $$ in terms of voltage $$ V $$ and current $$ I $$:

$$
P = V \cdot I
$$

Rearranging this gives:

$$
I = \frac{P}{V}
$$

Given that the minimum power output $$ P = 50 \, \text{mW} = 0.05 \, \text{W} $$ and the bias voltage $$ V = 6 \, \text{V} $$, we can substitute these values into the equation.
Now, we will calculate the required current using the formula derived in Step 1:

$$
I = \frac{0.05}{6}
$$

Now, I will perform the calculation.functions.calculate_or_simplify{"expression":"0.05/6","return_form":"decimal"}
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.05}{6}$$
- step1: Convert the expressions:
  $$\frac{\frac{1}{20}}{6}$$
- step2: Multiply by the reciprocal:
  $$\frac{1}{20}\times \frac{1}{6}$$
- step3: Multiply the fractions:
  $$\frac{1}{20\times 6}$$
- step4: Multiply:
  $$\frac{1}{120}$$
The required current for oscillation is approximately $$ 0.0083 \, \text{A} $$ or $$ 8.33 \, \text{mA} $$.
To calculate the resonant frequency $$ f $$ of the cavity, we can use the formula:

$$
f = \frac{c}{\lambda}
$$

where $$ c $$ is the speed of light (approximately $$ 3 \times 10^8 \, \text{m/s} $$) and $$ \lambda $$ is the wavelength. The wavelength can be related to the length of the cavity $$ L $$ by:

$$
\lambda = 2L
$$

Given that the length of the cavity $$ L = 2 \, \text{cm} = 0.02 \, \text{m} $$, we can find $$ \lambda $$ and then calculate the resonant frequency $$ f $$.
First, we calculate the wavelength:

$$
\lambda = 2 \times 0.02
$$

Then, we will calculate the resonant frequency using:

$$
f = \frac{3 \times 10^8}{\lambda}
$$

Now, I will perform these calculations.functions.calculate_or_simplify{"expression":"2*0.02","return_form":"decimal"}
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 0.02$$
- step1: Multiply the numbers:
  $$0.04$$
Calculate or simplify the expression $$ 3*10^8/0.04 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{3\times 10^{8}}{0.04}$$
- step1: Reduce the fraction:
  $$7.5\times 10^{9}$$
The wavelength $$ \lambda $$ is $$ 0.04 \, \text{m} $$, and the resonant frequency $$ f $$ of the cavity is $$ 7.5 \times 10^9 \, \text{Hz} $$ or $$ 7.5 \, \text{GHz} $$.
i) The required current for oscillation is approximately $$ 8.33 \, \text{mA} $$. ii) The resonant frequency of the cavity is $$ 7.5 \, \text{GHz} $$.

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