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ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
April 15, 2023 Dr Wazhar - FKM Kuktem 2
What is the meaning of single loop and multi-loop electrical network?
Single loop network(one mesh or current)
Multi-loop electrical network(more than one mesh or current)
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Creating transfer function of multi-loop electrical network
Steps:1. Decide input and output2. Obtain relationship between
voltage and current (Ohm’s law)
3. Convert to frequency domain4. Obtain transfer function
between output and input
Example 1
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 1: Decide input and output
Input:Supply voltage v(t)
Output:Capacitor voltage vc(t)
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 2: Write equations
(𝑖¿¿1 (𝑡 )−𝑖3 (𝑡 ))+( 𝑑𝑖1 (𝑡 )𝑑𝑡
−𝑑 𝑖2 (𝑡 )𝑑𝑡 )2+( 𝑖1 (𝑡 )−𝑖2 (𝑡 ))=𝑣 (𝑡)¿
Taking Laplace transform
)()1()21()22( 321 sVIIsIs
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 2: Write equations
4( 𝑑𝑖2 (𝑡 )𝑑𝑡
−𝑑𝑖3 (𝑡 )𝑑𝑡 )+3( 𝑑𝑖2 (𝑡 )
𝑑𝑡 )+ (𝑖2 (𝑡 )−𝑖1 (𝑡 ) )+2( 𝑑𝑖2 (𝑡 )𝑑𝑡
−𝑑𝑖1 (𝑡 )𝑑𝑡 )=0
Taking Laplace Transform
0)4()91()21( 321 IsIsIs
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 2: Write equations
4( 𝑑𝑖3 (𝑡 )𝑑𝑡
−𝑑𝑖2 (𝑡 )𝑑𝑡 )+1∫ 𝑖3 (𝑡 )𝑑𝑡+(𝑖3 (𝑡 )− 𝑖1 (𝑡 ) )=0
Taking Laplace Transform
0)11
4()4()1( 321 Is
sIsI
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Alternatively the circuit can be written in s-domain directly (OPTIONAL)
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 3: Obtain relationship between voltage and current (Ohm’s Law)
0)11
4()4()1( 321 Is
sIsI
0)4()91()21( 321 IsIsIs
)()1()21()22( 321 sVIIsIs
0
0
)(
)14(41
4)19()12(
1)12()22(
3
2
1
2
sV
I
I
I
s
sss
sss
ss
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 4: Obtain transfer function between output and input
)(
)(
sVOutput
sVInput
c
)(1
)( 3 sIssVc
0
0
)(
)14(41
4)19()12(
1)12()22(
3
2
1
2
sV
I
I
I
s
sss
sss
ss
Need to solve this simultaneous equations for I3
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 4: Obtain transfer function between output and input
0
0
)(
)14(41
4)19()12(
1)12()22(
3
2
1
2
sV
I
I
I
s
sss
sss
ss
sss
s
sss
ss
s
ss
sVss
sI
)14(41
4)19()12(
1)12()22(
041
0)19()12(
)()12()22(
)(
2
3
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Step 4: Obtain transfer function between output and input
132207722
)1138()(
423
2
3
ssss
sssVsI
)(1
)( 3 sIssVc
132207722
1138
)(
)(
)(
)()(
423
2
ssss
ss
sV
sV
sR
sCsG C
Therefore,
Since,
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Example 2
Find the transfer function VL(s)/V(s)
Redrawing the circuit in s-domain
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Example 3
Find the transfer function X1(s)/U(s) and X2(s)/U(s).
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Example 4
Determine the transfer function Y2(s)/F(s)