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Chapter 16: Problem 12

Determine \(T_{1}\) for a varactor diode if \(C_{0}=22 \mathrm{pF}, T C_{C}=0.02 \% /{ }^{\circ} \mathrm{C}\), and \(\Delta C=0.11 \mathrm{pF}\) due to an increase in temperature above \(T_{0}=25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The value of \(T_1\) can be calculated by performing the arithmetic in Step 5. This answer represents the temperature at which the given change in capacitance occurs in the varactor diode.

Step by step solution

01

Identify the Relevant Parameters

From the problem, the important parameters are as follows: Capacitance at Temperature \(T_0\), \(C_0 = 22\, pF\); Temperature Coefficient, \(TC_C = 0.02\% / ^{\circ}C\); The change in Capacitance, \(\Delta C = 0.11\, pF\); and the reference Temperature, \(T_0 = 25^{\circ}C\)
02

Use the Capacitance Change Formula

The formula for change in capacitance with temperature is given by: \(\Delta C = TC_C * C_0 * (T_1 - T_0)\). Here, \(\Delta C\) is the change in capacitance, \(TC_C\) is the temperature coefficient of capacitance, \(C_0\) is the initial capacitance, \(T_1\) is the final temperature (which we are seeking), and \(T_0\) is the initial temperature.
03

Rearrange the Formula for \(T_1\)

We rearrange the formula to solve for the final temperature \(T_1\). The rearranged formula becomes: \(T_1 = \Delta C / (TC_C * C_0) + T_0\)
04

Substitute the Values into the Formula

Now, we substitute the given values into the rearranged formula: \(T_1 = 0.11 pF / (0.02% * 22 pF) + 25^{\circ}C\). But before substituting, remember that \(0.02\% = 0.02/100 = 0.0002\) since the temperature coefficient is given as a percentage.
05

Calculate the Value of \(T_1\)

On substituting the values and calculating, the value of the final temperature \(T_1\) can be determined.

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