EMG 4076: Electromagnetic Interference
Tutorial 2: Coupling and Shielding 1. The circuit of Figure Q1 represents the capacitive coupling between two circuits with a common ground return. (a) Derive the expression for the noise voltage VN. jVS (b) Express VN in the form of V N = K ( j + sa )( j + sb ) (c) Using the appropriate simplification of the equation, explain the effects at low frequencies and at mid frequencies if the termination resistance R2S is decreased.
C1 I1 R1L
VS
C2 I2 R2S R2L VN
R1S +
VS
I1 I2
L11 M12 L22 R2S LG R2L + VN R1L
R1S
CG
Figure Q1
Figure Q2
2. The circuit of Figure Q2 represents the inductive coupling between two circuits with a common ground return. (a) Derive the expression for the noise voltage VN. jVS (b) Express VN in the form of V N = K ( j + sa )( j + sb ) (c) Using the appropriate simplification of the equation, explain the effects at low frequencies and at mid frequencies if the termination resistance R2S is decreased.
3.
Consider three parallel wires, two are the signal leads (lead-1 and lead-2) and the third is a common signal-return lead (lead-G). Lead-1 is shielded with a coaxial sleeve. The shield is grounded with a pigtail lead. (a) Draw the equivalent circuit when lead-1 is the EMI source. (b) Assuming the source resistance of the signal source of lead-1 is negligible, find the expression for the noise voltage on lead-2. Include the effect of pigtail-lead inductance. (c) Draw the equivalent circuit when the shield is applied on lead-2 (instead of lead1). Find the expression for the noise voltage on lead-2. Include the effect of pigtail-lead inductance.
Chapter 2: Coupling and Shielding
EMG 4076: Electromagnetic Interference
4.
The circuit of Figure Q2 represents the inductive coupling between two circuits with a common ground return. (a) If lead-2 is shielded to reduce magnetic coupling, draw the equivalent circuit. (b) Find the expression for the noise voltage across R2L. Include the effect of shield resistance. State all the assumptions made in order to simplify the equation.
5.
Shielding effectiveness is given by S = 20 log
VN VN
no shield shield
. Based on your
expression in question 2 (a) and 4 (b), show that the shielding effectiveness can be jLS expressed as S = 20 log 1 + , when the load resistances are assumed to be RS large. 6. Consider a three-wire configuration as shown in Figure Q6. Conductor 1 is connected to a high voltage analog signal (VS=10V) with R1S=100 and R1L=2k. Conductor 2 is carrying a low voltage analog signal with R2S=R2L=50. G is the common ground connection. The diameter d of the conductors is 0.5mm, spacing D12=10mm and D1G=D2G=20mm. The length of each wire is 100mm. The insulators around the conductors have a dielectric constant of 8. Assume all the equations derived earlier can be used in this case. Make any assumptions that will make your calculations easy.
1 D12 2
r=8
D1G G D\2G
Figure Q6 (a) Calculate approximate values for C1, C2 and CG (as in Figure Q1). (b) Determine the maximum noise voltage on conductor 2 due to capacitive coupling only. (c) Sketch the frequency response for the above condition. (d) It is required that the noise magnitude in wire 2 must be less than 0.8 volts. Is this requirement satisfied? If no, suggest any possible remedy to reduce the noise voltage.
Chapter 2: Coupling and Shielding
EMG 4076: Electromagnetic Interference
7.
Consider the same three-wire configuration as in question 6. (a) Determine approximate values for L1, L2 and L12 (L1=L11+LG, L2=L22+LG, L12=M12+LG of Figure Q2). (b) Determine the maximum noise voltage VN due to inductive coupling only. (c) Calculate the total noise (with inductive and capacitive couplings) on conductor 2 (for the worst-case). Hint: L1C1G , m = l 2 / v 2
(L1 + L2 2 L12 )C12,m
v= c
= l 2 / v2
where c = 3 108 m/s is the wave propagation velocity.
Chapter 2: Coupling and Shielding
