Characteristic Impedance using Sending End Voltage (LTL) Calculator

✖Sending end voltage is the voltage at the sending end of a long transmission line.ⓘ Sending End Voltage [V_s]			+10% -10%
✖Receiving end voltage is the voltage developed at the receiving end of a long transmission line.ⓘ Receiving End Voltage [V_r]			+10% -10%
✖Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.ⓘ Propagation Constant [γ]			+10% -10%
✖Length is defined as the end to end distance of the conductor used in a long transmission line.ⓘ Length [L]			+10% -10%
✖Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.ⓘ Receiving End Current [I_r]			+10% -10%

✖Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.ⓘ Characteristic Impedance using Sending End Voltage (LTL) [Z₀]

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Characteristic Impedance using Sending End Voltage (LTL) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current)
Z₀ = (V_s-V_r*cosh(γ*L))/(sinh(γ*L)*I_r)
This formula uses 2 Functions, 6 Variables

Functions Used

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., 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., cosh(Number)

Variables Used

Characteristic Impedance - (Measured in Ohm) - Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.
Sending End Voltage - (Measured in Volt) - Sending end voltage is the voltage at the sending end of a long transmission line.
Receiving End Voltage - (Measured in Volt) - Receiving end voltage is the voltage developed at the receiving end of a long transmission line.
Propagation Constant - Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.
Length - (Measured in Meter) - Length is defined as the end to end distance of the conductor used in a long transmission line.
Receiving End Current - (Measured in Ampere) - Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.

STEP 1: Convert Input(s) to Base Unit

Sending End Voltage: 189.57 Kilovolt --> 189570 Volt (Check conversion here)
Receiving End Voltage: 8.88 Kilovolt --> 8880 Volt (Check conversion here)
Propagation Constant: 1.24 --> No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required
Receiving End Current: 6.19 Ampere --> 6.19 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z₀ = (V_s-V_r*cosh(γ*L))/(sinh(γ*L)*I_r) --> (189570-8880*cosh(1.24*3))/(sinh(1.24*3)*6.19)

Evaluating ... ...

Z₀ = 48.9546754711376

STEP 3: Convert Result to Output's Unit

48.9546754711376 Ohm --> No Conversion Required

FINAL ANSWER

48.9546754711376 ≈ 48.95468 Ohm <-- Characteristic Impedance

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power System » Transmission Lines » Long Transmission Line » Impedance and Admittance » Characteristic Impedance using Sending End Voltage (LTL)

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< Impedance and Admittance Calculators

Characteristic Impedance using B Parameter (LTL)

LaTeX Go Characteristic Impedance = B Parameter/(sinh(Propagation Constant*Length))

Characteristic Impedance using C Parameter (LTL)

LaTeX Go Characteristic Impedance = 1/C Parameter*sinh(Propagation Constant*Length)

Impedance using Characteristic Impedance (LTL)

LaTeX Go Impedance = Characteristic Impedance^2*Admittance

Impedance using Propagation Constant (LTL)

LaTeX Go Impedance = Propagation Constant^2/Admittance

Characteristic Impedance using Sending End Voltage (LTL) Formula

LaTeX Go

Which is the type of long transmission line?

A power transmission line with its effective length of around 250 Kms or above is referred to as a long transmission line. The line constants are uniformly distributed over the entire length of the line.

How to Calculate Characteristic Impedance using Sending End Voltage (LTL)?

Characteristic Impedance using Sending End Voltage (LTL) calculator uses Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current) to calculate the Characteristic Impedance, The Characteristic Impedance using Sending End Voltage (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 calculate Characteristic Impedance using Sending End Voltage (LTL) using this online calculator? To use this online calculator for Characteristic Impedance using Sending End Voltage (LTL), enter Sending End Voltage (V_s), Receiving End Voltage (V_r), Propagation Constant (γ), Length (L) & Receiving End Current (I_r) and hit the calculate button. Here is how the Characteristic Impedance using Sending End Voltage (LTL) calculation can be explained with given input values -> 48.95468 = (189570-8880*cosh(1.24*3))/(sinh(1.24*3)*6.19).

FAQ

What is Characteristic Impedance using Sending End Voltage (LTL)?

The Characteristic Impedance using Sending End Voltage (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 and is represented as Z₀ = (V_s-V_r*cosh(γ*L))/(sinh(γ*L)*I_r) or Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current). Sending end voltage is the voltage at the sending end of a long transmission line, Receiving end voltage is the voltage developed at the receiving end of a long transmission line, Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line, Length is defined as the end to end distance of the conductor used in a long transmission line & Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.

How to calculate Characteristic Impedance using Sending End Voltage (LTL)?

The Characteristic Impedance using Sending End Voltage (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 is calculated using Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current). To calculate Characteristic Impedance using Sending End Voltage (LTL), you need Sending End Voltage (V_s), Receiving End Voltage (V_r), Propagation Constant (γ), Length (L) & Receiving End Current (I_r). With our tool, you need to enter the respective value for Sending End Voltage, Receiving End Voltage, Propagation Constant, Length & Receiving End Current and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Characteristic Impedance?

In this formula, Characteristic Impedance uses Sending End Voltage, Receiving End Voltage, Propagation Constant, Length & Receiving End Current. We can use 3 other way(s) to calculate the same, which is/are as follows -

Characteristic Impedance = B Parameter/(sinh(Propagation Constant*Length))
Characteristic Impedance = 1/C Parameter*sinh(Propagation Constant*Length)
Characteristic Impedance = sqrt(Impedance/Admittance)

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