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Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line. Check FAQs
Z0=Vr⋅sinh(γ⋅L)Is-Ir⋅cosh(γ⋅L)
Z0 - Characteristic Impedance?Vr - Receiving End Voltage?γ - Propagation Constant?L - Length?Is - Sending End Current?Ir - Receiving End Current?

Characteristic Impedance using Sending End Current (LTL) Example

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With units
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Here is how the Characteristic Impedance using Sending End Current (LTL) equation looks like with Values.

Here is how the Characteristic Impedance using Sending End Current (LTL) equation looks like with Units.

Here is how the Characteristic Impedance using Sending End Current (LTL) equation looks like.

48.989Edit=8.88Edit⋅sinh(1.24Edit⋅3Edit)3865.49Edit-6.19Edit⋅cosh(1.24Edit⋅3Edit)
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Characteristic Impedance using Sending End Current (LTL) Solution

Follow our step by step solution on how to calculate Characteristic Impedance using Sending End Current (LTL)?

FIRST Step Consider the formula
Z0=Vr⋅sinh(γ⋅L)Is-Ir⋅cosh(γ⋅L)
Next Step Substitute values of Variables
∴ Z0=8.88kV⋅sinh(1.24⋅3m)3865.49A-6.19A⋅cosh(1.24⋅3m)
Next Step Convert Units
∴ Z0=8880V⋅sinh(1.24⋅3m)3865.49A-6.19A⋅cosh(1.24⋅3m)
Next Step Prepare to Evaluate
∴ Z0=8880⋅sinh(1.24⋅3)3865.49-6.19⋅cosh(1.24⋅3)
Next Step Evaluate
∴Z0=48.9890114066324Ω
LAST Step Rounding Answer
∴Z0=48.989Ω

Characteristic Impedance using Sending End Current (LTL) Formula Elements

Variables
Functions
Characteristic Impedance
Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.
Symbol: Z0
Measurement: Electric ResistanceUnit: Ω
Note: Value should be greater than 0.
Formulas to find Characteristic ImpedanceOpen Variable
Receiving End Voltage
Receiving end voltage is the voltage developed at the receiving end of a long transmission line.
Symbol: Vr
Measurement: Electric PotentialUnit: kV
Note: Value can be positive or negative.
Formulas to find Receiving End VoltageOpen Variable
Propagation Constant
Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.
Symbol: γ
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Propagation ConstantOpen Variable
Length
Length is defined as the end to end distance of the conductor used in a long transmission line.
Symbol: L
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find LengthOpen Variable
Sending End Current
Sending end current is the voltage at the sending end of a short transmission line.
Symbol: Is
Measurement: Electric CurrentUnit: A
Note: Value can be positive or negative.
Formulas to find Sending End CurrentOpen Variable
Receiving End Current
Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.
Symbol: Ir
Measurement: Electric CurrentUnit: A
Note: Value can be positive or negative.
Formulas to find Receiving End CurrentOpen Variable
sinh
The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function.
Syntax: sinh(Number)
cosh
The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2.
Syntax: cosh(Number)

Other Formulas to find Characteristic Impedance

​Go Characteristic Impedance using B Parameter (LTL)
Z0=Bsinh(γ⋅L)
​Go Characteristic Impedance using C Parameter (LTL)
Z0=1C⋅sinh(γ⋅L)
​Go Characteristic Impedance (LTL)
Z0=ZY
​Go Characteristic Impedance using Sending End Voltage (LTL)
Z0=Vs-Vr⋅cosh(γ⋅L)sinh(γ⋅L)⋅Ir

Other formulas in Impedance and Admittance category

​Go Impedance using Characteristic Impedance (LTL)
Z=Z02⋅Y
​Go Impedance using Propagation Constant (LTL)
Z=γ2Y
​Go Surge Impedance (LTL)
Zs=LHenryCFarad
​Go Admittance using Characteristic Impedance (LTL)
Y=ZZ02

How to Evaluate Characteristic Impedance using Sending End Current (LTL)?

Characteristic Impedance using Sending End Current (LTL) evaluator uses Characteristic Impedance = (Receiving End Voltage*sinh(Propagation Constant*Length))/(Sending End Current-Receiving End Current*cosh(Propagation Constant*Length)) to evaluate the Characteristic Impedance, The Characteristic Impedance using Sending End Current (LTL) formula is defined as a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line. Characteristic Impedance is denoted by Z0 symbol.

How to evaluate Characteristic Impedance using Sending End Current (LTL) using this online evaluator? To use this online evaluator for Characteristic Impedance using Sending End Current (LTL), enter Receiving End Voltage (Vr), Propagation Constant (γ), Length (L), Sending End Current (Is) & Receiving End Current (Ir) and hit the calculate button.

FAQs on Characteristic Impedance using Sending End Current (LTL)

What is the formula to find Characteristic Impedance using Sending End Current (LTL)?
The formula of Characteristic Impedance using Sending End Current (LTL) is expressed as Characteristic Impedance = (Receiving End Voltage*sinh(Propagation Constant*Length))/(Sending End Current-Receiving End Current*cosh(Propagation Constant*Length)). Here is an example- 48.98901 = (8880*sinh(1.24*3))/(3865.49-6.19*cosh(1.24*3)).
How to calculate Characteristic Impedance using Sending End Current (LTL)?
With Receiving End Voltage (Vr), Propagation Constant (γ), Length (L), Sending End Current (Is) & Receiving End Current (Ir) we can find Characteristic Impedance using Sending End Current (LTL) using the formula - Characteristic Impedance = (Receiving End Voltage*sinh(Propagation Constant*Length))/(Sending End Current-Receiving End Current*cosh(Propagation Constant*Length)). This formula also uses Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).
What are the other ways to Calculate Characteristic Impedance?
Here are the different ways to Calculate Characteristic Impedance-
  • Characteristic Impedance=B Parameter/(sinh(Propagation Constant*Length))OpenImg
  • Characteristic Impedance=1/C Parameter*sinh(Propagation Constant*Length)OpenImg
  • Characteristic Impedance=sqrt(Impedance/Admittance)OpenImg
Can the Characteristic Impedance using Sending End Current (LTL) be negative?
No, the Characteristic Impedance using Sending End Current (LTL), measured in Electric Resistance cannot be negative.
Which unit is used to measure Characteristic Impedance using Sending End Current (LTL)?
Characteristic Impedance using Sending End Current (LTL) is usually measured using the Ohm[Ω] for Electric Resistance. Megohm[Ω], Microhm[Ω], Volt per Ampere[Ω] are the few other units in which Characteristic Impedance using Sending End Current (LTL) can be measured.
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