Electronics Assignment Solution - Circuit Analysis and Design

This document presents a comprehensive solution to an electronics assignment, focusing on circuit analysis and design principles. The solution begins by calculating the capacitance at a resonant frequency, providing a step-by-step breakdown of the formula and the resulting value. It then delves into inductance calculations for a coil, determining the number of turns required for different core materials, specifically comparing air and manganese zinc cores. Finally, the assignment addresses capacitance calculations for two different frequencies, providing the resulting capacitance values in pico farads. The solution incorporates relevant formulas and provides a clear explanation of each step. The assignment includes references to patents and research papers related to wireless radio technology and sensing systems, showing the practical applications of the concepts discussed.

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(a) At resonant frequency
ω= 1
√ LC
2 πf = 1
√LC
4 π 2 f 2= 1
LC
C= 1
4 π2 f 2 L
C= 1
4 π2 ×8 ×1982 ×103
C=9.79 ×10−11
Value of v2
¿ v1 × rms
R × 1
ωc
¿ 100 μv
300 × 1012
2 π × 198× 103 × 79.7
¿ 100 × 106
30× 2 π ×198 ×103 ×79.7
¿ 3.361× 10−2 V
¿ 0.03361 V
(b) L= μ N2 A
μ

N2= Lμ
μA ; N = √ Lμ
μA
N= √ 8 ×10−3 ×50 × 10−3
1.256629× 10−6 × π ×7.5 ×10−3 ×7.5 × 10−3
¿ √ 400× 10−6
222 ×10−12 ; → √ 400
222 ×106
N=1.342 ×103=1342
In case of rod of manganese zinc
N= √ 6 × 10−3 × 50 ×10−3
6 ×10−4 × π × 7.5 ×10−3 ×7.5 ×10−3
N= √ 0.29294 × 104
N=0.53× 102 ;=53
(c)
C1= 1
4 π2 f 1
2 L = 1
4 π 2 ( 148 )2 ×106 ×8 ×10−3
C1=1.4267 ×10−10
C1=142.67 pico farad
C2= 1
4 π2 f 2 L= 1
4 π 2 × ( 248 ) 2 ×106 × 8 ×10−3
C2=5.08 ×10−11 ;5.08 pico farad

References

Jain, M., Choi, J. I., Srinivasan, K., Levis, P., Katti, S., & Seth, S. (2018). U.S. Patent No.
9,887,728. Washington, DC: U.S. Patent and Trademark Office
Polehn, Donna L. "Wireless radio extension using up-and down-conversion." U.S. Patent No.
9,473,187. 18 Oct. 2016
Spenza, D., Magno, M., Basagni, S., Benini, L., Paoli, M., & Petrioli, C. (2015, April). Beyond
duty cycling: Wake-up radio with selective awakenings for long-lived wireless sensing
systems. In 2015 IEEE Conference on Computer Communications (INFOCOM) (pp. 522-
530). IEEE
Toncich, S. S., & Coan, P. D. (2015). U.S. Patent No. 8,929,957. Washington, DC: U.S. Patent
and Trademark Office