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Characteristic Impedance using Sending End Voltage (LTL) Formula

GoCharacteristic Impedance using B Parameter (LTL) Formula

GoCharacteristic Impedance using C Parameter (LTL) Formula

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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

Z 0 = \frac{V s - V r \cdot \cosh (γ \cdot L)}{\sinh (γ \cdot L) \cdot I r}

Z₀ - Characteristic Impedance?V_s - Sending End Voltage?V_r - Receiving End Voltage?γ - Propagation Constant?L - Length?I_r - Receiving End Current?

Characteristic Impedance using Sending End Voltage (LTL) Example

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

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

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

48.9547 = \frac{189.57 - 8.88 \cdot \cosh (1.24 \cdot 3)}{\sinh (1.24 \cdot 3) \cdot 6.19}

48.9547Ω = \frac{189.57kV - 8.88kV \cdot \cosh (1.24 \cdot 3m)}{\sinh (1.24 \cdot 3m) \cdot 6.19A}

48.9547 = \frac{189.57 - 8.88 \cdot \cosh (1.24 \cdot 3)}{\sinh (1.24 \cdot 3) \cdot 6.19}

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Characteristic Impedance using Sending End Voltage (LTL) Solution

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

FIRST Step Consider the formula

Z 0 = \frac{V s - V r \cdot \cosh (γ \cdot L)}{\sinh (γ \cdot L) \cdot I r}

Next Step Substitute values of Variables

∴

Z 0 = \frac{189.57kV - 8.88kV \cdot \cosh (1.24 \cdot 3m)}{\sinh (1.24 \cdot 3m) \cdot 6.19A}

Next Step Convert Units

∴

Z 0 = \frac{189570V - 8880V \cdot \cosh (1.24 \cdot 3m)}{\sinh (1.24 \cdot 3m) \cdot 6.19A}

Next Step Prepare to Evaluate

∴

Z 0 = \frac{189570 - 8880 \cdot \cosh (1.24 \cdot 3)}{\sinh (1.24 \cdot 3) \cdot 6.19}

Next Step Evaluate

∴

Z 0 = 48.9546754711376Ω

LAST Step Rounding Answer

∴

Z 0 = 48.9547Ω

Characteristic Impedance using Sending End Voltage (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 Impedance

Sending End Voltage

Sending end voltage is the voltage at the sending end of a long transmission line.

Symbol: V_s

Measurement: Electric PotentialUnit: kV

Note: Value can be positive or negative.

Formulas to find Sending End Voltage

Receiving End Voltage

Receiving end voltage is the voltage developed at the receiving end of a long transmission line.

Symbol: V_r

Measurement: Electric PotentialUnit: kV

Note: Value can be positive or negative.

Formulas to find Receiving End Voltage

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 Constant

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 Length

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: I_r

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Receiving End Current

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)

Z 0 = \frac{B}{\sinh (γ \cdot L)}

Go Characteristic Impedance using C Parameter (LTL)

Z 0 = \frac{1}{C} \cdot \sinh (γ \cdot L)

Go Characteristic Impedance (LTL)

Z 0 = \sqrt{\frac{Z}{Y}}

Go Characteristic Impedance using Sending End Current (LTL)

Z 0 = \frac{V r \cdot \sinh (γ \cdot L)}{I s - I r \cdot \cosh (γ \cdot L)}

Other formulas in Impedance and Admittance category

Go Impedance using Characteristic Impedance (LTL)

Z = {Z 0}^{2} \cdot Y

Go Impedance using Propagation Constant (LTL)

Z = \frac{γ^{2}}{Y}

Go Surge Impedance (LTL)

Zs = \sqrt{\frac{L Henry}{C Farad}}

Go Admittance using Characteristic Impedance (LTL)

Y = \frac{Z}{{Z 0}^{2}}

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

Characteristic Impedance using Sending End Voltage (LTL) evaluator uses Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current) to evaluate 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 evaluate Characteristic Impedance using Sending End Voltage (LTL) using this online evaluator? To use this online evaluator 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.

FAQs on Characteristic Impedance using Sending End Voltage (LTL)

What is the formula to find Characteristic Impedance using Sending End Voltage (LTL)?

The formula of Characteristic Impedance using Sending End Voltage (LTL) is expressed as Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current). Here is an example- 48.95468 = (189570-8880*cosh(1.24*3))/(sinh(1.24*3)*6.19).

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

With Sending End Voltage (V_s), Receiving End Voltage (V_r), Propagation Constant (γ), Length (L) & Receiving End Current (I_r) we can find Characteristic Impedance using Sending End Voltage (LTL) using the formula - Characteristic Impedance = (Sending End Voltage-Receiving End Voltage*cosh(Propagation Constant*Length))/(sinh(Propagation Constant*Length)*Receiving End Current). 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))
Characteristic Impedance=1/C Parameter*sinh(Propagation Constant*Length)
Characteristic Impedance=sqrt(Impedance/Admittance)

Can the Characteristic Impedance using Sending End Voltage (LTL) be negative?

No, the Characteristic Impedance using Sending End Voltage (LTL), measured in Electric Resistance cannot be negative.

Which unit is used to measure Characteristic Impedance using Sending End Voltage (LTL)?

Characteristic Impedance using Sending End Voltage (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 Voltage (LTL) can be measured.

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Characteristic Impedance using Sending End Voltage (LTL) Formula

​GoCharacteristic Impedance using B Parameter (LTL) Formula

​GoCharacteristic Impedance using C Parameter (LTL) Formula

Characteristic Impedance using Sending End Voltage (LTL) Example

Characteristic Impedance using Sending End Voltage (LTL) Solution

Characteristic Impedance using Sending End Voltage (LTL) Formula Elements

Other Formulas to find Characteristic Impedance

Other formulas in Impedance and Admittance category

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

FAQs on Characteristic Impedance using Sending End Voltage (LTL)

Variable Name

GoCharacteristic Impedance using B Parameter (LTL) Formula

GoCharacteristic Impedance using C Parameter (LTL) Formula