Numerical on Noise - Basic Communication System - Communication Engineering

TL;DR

Calculate the thermal noise in resistors with different configurations using the formula en = 4ktVR.

Transcript

hello friends now we will see the numerical on noise here the problem it is defined to resistor 20 kilo ohm and 50 km are at room temperature that is 290 degree kelvin calculate for the bandwidth of 100 kilohertz the thermal noise for the following conditions first condition is that for each resistor second condition for two resistors in series thi... Read More

Key Insights

• 😇 The thermal noise in a resistor can be calculated using the formula en = 4ktVR.
• ⚡ The thermal noise voltage increases with increasing temperature and bandwidth.
• 🔂 The thermal noise in a resistor can be different in various configurations, such as single resistors, series combinations, and parallel combinations.
• 🫚 In series combinations of resistors, the thermal noise increases with the square root of the total resistance.

Questions & Answers

Q: What is the formula for calculating thermal noise in a resistor?

The formula for calculating thermal noise in a resistor is en = 4ktVR, where en is the thermal noise voltage, k is the Boltzmann constant, t is the temperature in Kelvin, V is the effective noise bandwidth, and R is the resistance.

Q: How do you calculate thermal noise in a 20 kilo ohm resistor?

To calculate thermal noise in a 20 kilo ohm resistor, you can use the formula en^2 = 4ktVR. Substituting the given values, en^2 = 4 * (1.38 * 10^-23) * 290 * (100 * 10^3) * (20 * 10^3). Solving this equation gives en = 5.66 microvolts.

Q: What is the thermal noise in a series combination of a 50 kilo ohm resistor and a 20 kilo ohm resistor?

In series combination, the net resistance is given by R = R1 + R2, which is 50 kilo ohm + 20 kilo ohm = 70 kilo ohm. Using the formula en = 5.66 * sqrt(R/20), we can calculate the thermal noise as en = 10.59 microvolts.

Q: How do you calculate the thermal noise in a parallel combination of a 20 kilo ohm resistor and a 50 kilo ohm resistor?

To calculate the thermal noise in a parallel combination, first find the equivalent resistance, Rp = (R1 * R2) / (R1 + R2), which is (20 * 50) / (20 + 50) = 100/7 kilo ohm. Then, use the formula en = 5.66 * sqrt(100/(20*7)) to calculate the thermal noise as en = 4.78 microvolts.

Summary & Key Takeaways

• The content demonstrates how to calculate thermal noise in resistors based on different configurations.

• It provides calculations for thermal noise in a single 20 kilo ohm resistor and a single 50 kilo ohm resistor.

• It also covers the calculations for thermal noise in two resistors in series and two resistors in parallel.