- Last updated

- Save as PDF

- Page ID
- 1483

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

In DC and low-frequency AC circuits, the characteristic impedance of parallel wires is usually ignored. This includes the use of coaxial cables in instrument circuits, often employed to protect weak voltage signals from being corrupted by induced “noise” caused by stray electric and magnetic fields. This is due to the relatively short timespans in which reflections take place in the line, as compared to the period of the waveforms or pulses of the significant signals in the circuit. As we saw in the last section, if a transmission line is connected to a DC voltage source, it will behave as a resistor equal in value to the line’s characteristic impedance only for as long as it takes the incident pulse to reach the end of the line and return as a reflected pulse, back to the source. After that time (a brief 16.292 µs for the mile-long coaxial cable of the last example), the source “sees” only the terminating impedance, whatever that may be.

If the circuit in question handles low-frequency AC power, such short time delays introduced by a transmission line between when the AC source outputs a voltage peak and when the source “sees” that peak loaded by the terminating impedance (round-trip time for the incident wave to reach the line’s end and reflect back to the source) are of little consequence. Even though we know that signal magnitudes along the line’s length are not equal at any given time due to signal propagation at (nearly) the speed of light, the actual phase difference between start-of-line and end-of-line signals is negligible, because line-length propagations occur within a very small fraction of the AC waveform’s period. For all practical purposes, we can say that voltage along all respective points on a low-frequency, two-conductor line are equal and in-phase with each other at any given point in time.

In these cases, we can say that the transmission lines in question are *electrically short*, because their propagation effects are much quicker than the periods of the conducted signals. By contrast, an *electrically long* line is one where the propagation time is a large fraction or even a multiple of the signal period. A “long” line is generally considered to be one where the source’s signal waveform completes at least a quarter-cycle (90^{o} of “rotation”) before the incident signal reaches line’s end. Up until this chapter in the *Lessons In Electric Circuits* book series, all connecting lines were assumed to be electrically short.

To put this into perspective, we need to express the distance traveled by a voltage or current signal along a transmission line in relation to its source frequency. An AC waveform with a frequency of 60 Hz completes one cycle in 16.66 ms. At light speed (186,000 mile/s), this equates to a distance of 3100 miles that a voltage or current signal will propagate in that time. If the velocity factor of the transmission line is less than 1, the propagation velocity will be less than 186,000 miles per second, and the distance less by the same factor. But even if we used the coaxial cable’s velocity factor from the last example (0.66), the distance is still a very long 2046 miles! Whatever distance we calculate for a given frequency is called the *wavelength*of the signal.

A simple formula for calculating wavelength is as follows:

The lower-case Greek letter “lambda” (λ) represents wavelength, in whatever unit of length used in the velocity figure (if miles per second, then wavelength in miles; if meters per second, then wavelength in meters). Velocity of propagation is usually the speed of light when calculating signal wavelength in open air or in a vacuum, but will be less if the transmission line has a velocity factor less than 1.

If a “long” line is considered to be one at least 1/4 wavelength in length, you can see why all connecting lines in the circuits discussed thusfar have been assumed “short.” For a 60 Hz AC power system, power lines would have to exceed 775 miles in length before the effects of propagation time became significant. Cables connecting an audio amplifier to speakers would have to be over 4.65 miles in length before line reflections would significantly impact a 10 kHz audio signal!

When dealing with radio-frequency systems, though, transmission line length is far from trivial. Consider a 100 MHz radio signal: its wavelength is a mere 9.8202 feet, even at the full propagation velocity of light (186,000 mile/s). A transmission line carrying this signal would not have to be more than about 2-1/2 feet in length to be considered “long!” With a cable velocity factor of 0.66, this critical length shrinks to 1.62 feet.

When an electrical source is connected to a load via a “short” transmission line, the load’s impedance dominates the circuit. This is to say, when the line is short, its own characteristic impedance is of little consequence to the circuit’s behavior. We see this when testing a coaxial cable with an ohmmeter: the cable reads “open” from center conductor to outer conductor if the cable end is left unterminated. Though the line acts as a resistor for a very brief period of time after the meter is connected (about 50 Ω for an RG-58/U cable), it immediately thereafter behaves as a simple “open circuit:” the impedance of the line’s open end. Since the combined response time of an ohmmeter and the human being using it *greatly exceeds* the round-trip propagation time up and down the cable, it is “electrically short” for this application, and we only register the terminating (load) impedance. It is the extreme speed of the propagated signal that makes us unable to detect the cable’s 50 Ω transient impedance with an ohmmeter.

If we use a coaxial cable to conduct a DC voltage or current to a load, and no component in the circuit is capable of measuring or responding quickly enough to “notice” a reflected wave, the cable is considered “electrically short” and its impedance is irrelevant to circuit function. Note how the electrical “shortness” of a cable is relative to the application: in a DC circuit where voltage and current values change slowly, nearly any physical length of cable would be considered “short” from the standpoint of characteristic impedance and reflected waves. Taking the same length of cable, though, and using it to conduct a high-frequency AC signal could result in a vastly different assessment of that cable’s “shortness!”

When a source is connected to a load via a “long” transmission line, the line’s own characteristic impedance dominates over load impedance in determining circuit behavior. In other words, an electrically “long” line acts as the principal component in the circuit, its own characteristics overshadowing the load’s. With a source connected to one end of the cable and a load to the other, current drawn from the source is a function primarily of the line and not the load. This is increasingly true the longer the transmission line is. Consider our hypothetical 50 Ω cable of infinite length, surely the ultimate example of a “long” transmission line: no matter what kind of load we connect to one end of this line, the source (connected to the other end) will only see 50 Ω of impedance, because the line’s infinite length prevents the signal from *ever reaching* the end where the load is connected. In this scenario, line impedance exclusively defines circuit behavior, rendering the load completely irrelevant.

The most effective way to minimize the impact of transmission line length on circuit behavior is to match the line’s characteristic impedance to the load impedance. If the load impedance is equal to the line impedance, then *any* signal source connected to the other end of the line will “see” the exact same impedance, and will have the exact same amount of current drawn from it, regardless of line length. In this condition of perfect impedance matching, line length only affects the amount of time delay from signal departure at the source to signal arrival at the load. However, perfect matching of line and load impedances is not always practical or possible.

The next section discusses the effects of “long” transmission lines, especially when line length happens to match specific fractions or multiples of signal wavelength.

## Review

- Coaxial cabling is sometimes used in DC and low-frequency AC circuits as well as in high-frequency circuits, for the excellent immunity to induced “noise” that it provides for signals.
- When the period of a transmitted voltage or current signal greatly exceeds the propagation time for a transmission line, the line is considered
*electrically short*. Conversely, when the propagation time is a large fraction or multiple of the signal’s period, the line is considered*electrically long*. - A signal’s
*wavelength*is the physical distance it will propagate in the timespan of one period. Wavelength is calculated by the formula λ=v/f, where “λ” is the wavelength, “v” is the propagation velocity, and “f” is the signal frequency. - A rule-of-thumb for transmission line “shortness” is that the line must be at least 1/4 wavelength before it is considered “long.”
- In a circuit with a “short” line, the terminating (load) impedance dominates circuit behavior. The source effectively sees nothing but the load’s impedance, barring any resistive losses in the transmission line.
- In a circuit with a “long” line, the line’s own characteristic impedance dominates circuit behavior. The ultimate example of this is a transmission line of infinite length: since the signal will
*never*reach the load impedance, the source only “sees” the cable’s characteristic impedance. - When a transmission line is terminated by a load precisely matching its impedance, there are no reflected waves and thus no problems with line length.

## FAQs

### What is effective length in transmission line? ›

The effective length of a short transmission line is **less than 80 km**. When the length of an overhead transmission line is up to about 50 km to 80 km and the line voltage is comparatively low (< 20 kV), it is usually considered as a short transmission line.

**How do you calculate transmission line? ›**

The positive-sequence inductive reactance is calculated by: x = 0.0628(ln 15.75 0.01495 + 1 4 )=0.453 ohm/km The power capacity of transmission line at 161 kV is: **P = 1612 × sin(30°) L × 0.453 MW where L = line length, km**.

**How do you calculate the size of a transmission line conductor? ›**

To calculate the Cable Sizing one needs to **divide the voltage running through the cable by the target current**. For instance, If your wire has a voltage current of 150 Volts and your target is 30 then you divide 150/30. This gives you your target resistance of 5 which is required.

**What are the sizes of transmission lines? ›**

**By length of the line**

- Lines shorter than 50 km are generally referred to as short transmission lines.
- Lines between 50 km and 150 km are generally referred to as medium transmission lines.
- Lines longer than 150 km are considered long transmission lines.

**Does transmission line length matter? ›**

**If the transmission line is short, the source now sees an input impedance that may not equal the characteristic impedance, instead seeing something closer to the load impedance**; if the source is not matched to this input impedance value, then there is reflection back into the source and you will not transfer maximum ...

**What is the minimum length of transmission line? ›**

A transmission line is defined as a short-length line if its length is less than **80 km (50 miles)**. In this case, the shut capacitance effect is negligible and only the resistance and inductive reactance are considered.

**What is the ideal value of transmission line? ›**

This is the ratio of the complex voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z_{0} are **50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission**.

**How many amps run through transmission lines? ›**

The largest transmission lines in use have a rating of over 4000 A per circuit, but **the average current in a typical circuit is more like 700 A**. Distribution lines typically have currents of hundreds of A or less.

**How do you calculate transmission line efficiency? ›**

**Which is the correct formula for the efficiency of a short transmission line (η %)**

- η % = (Power supplied / Power delivered × 100)
- η % = (Power delivered / Power supplied × 100)
- η % = (Power exhausted / Power delivered × 100)
- η % = (Power supplied / Power exhausted × 100)

**What size wire is used for transmission line? ›**

A commonly-encountered form of parallel wire transmission line is 300 Ω twin-lead. Although implementations vary, the **wire diameter is usually about 1 mm** and and the wire spacing is usually about 6 mm.

### How much voltage do transmission lines carry? ›

Transmission line voltages vary from **44,000 to over 765,000 volts**. The higher the voltage, the more electricity the line can carry.

**What size wire is used for transmission lines? ›**

0000 (or 4/0) for solid-type conductors. Solid wire is not usually made in sizes larger than 4/0, and **stranded wire for sizes larger than no.** **2** is generally used.

**Why are there 3 transmission lines? ›**

Using three wires instead of two **allows a greater utilization of the wires' current carrying capacity for more of the time**. In the diagram at the right, more current is flowing for more of the time. With 3 phase power, there are 3 alternating current sources (one between any 2 of the 3 wires).

**What is short transmission line? ›**

A short transmission line is defined as **a transmission line with an effective length less than 80 km (50 miles), or with a voltage less than 69 kV**. Unlike medium transmission lines and long transmission lines, the line charging current is negligible, and hence the shunt capacitance can be ignored.

**What is electrically short vs long? ›**

When the period of a transmitted voltage or current signal greatly exceeds the propagation time for a transmission line, the line is considered electrically short. Conversely, when the propagation time is a large fraction or multiple of the signal's period, the line is considered electrically long.

**What is the difference between short transmission line and long transmission line? ›**

**Short transmission line – The line length is up to 60 km and the line voltage is comparatively low less than 20KV**. 2. Medium transmission line – The line length is between 60 km to 160 km and the line voltage is between 20kV to 100kV.

**What is critical length? ›**

The critical length I, in composites is **a parameter which is an indicator of the amount of stress transferred to the fiber**: a fiber whose aspect ratio s = l/d, (where df is the fiber diameter) is much greater than the critical aspect ratio s, = l,/d.f strengthens the material, while a fiber whose aspect ratio is much ...

**Does the length of a transmission line affect impedance? ›**

**The impedance of a transmission line is proportional to its length** because the impedance is primarily determined by the distributed capacitance and inductance per unit length of the line.

**What is the regulation of transmission line? ›**

Voltage regulation of transmission line is defined as **the ratio of the difference between sending and receiving end voltage to receiving end voltage of a transmission line between conditions of no-load and full load**. Where V_{s} is the sending end voltage per phase and V_{R} is the receiving end voltage per phase.

**Which transmission line is better? ›**

**Underground cables** take up less right-of-way than overhead lines, have lower visibility, and are less affected by bad weather. Under grounding can increase the initial costs of electric power transmission and distribution but may decrease operational costs over the lifetime of the cables.

### What are the most important transmission line specifications? ›

The performance of transmission line depends on the parameters of the line. The transmission line has mainly four parameters, **resistance, inductance, capacitance and shunt conductance**.

**What is the most common current transmission range? ›**

The most popular form of signal transmission used in modern industrial instrumentation systems is the **4-20 mA DC standard**. This is an analog signal standard, meaning that the electric current is used to proportionately represent measurements or control signals.

**Is 125 amp service enough? ›**

**Most homes require an electrical service of at least 100 amps**. This is also the minimum panel amperage required by the National Electrical Code (NEC). A 100-amp service panel will typically provide enough power for a medium-sized home that includes several 240-volt appliances and central air-conditioning.

**What limits the capacity of a transmission line? ›**

Typically, for very long lines, the power flow must be limited to what is commonly called the **Surge Impedance Loading (SIL) of the line**. Surge Impedance Loading is equal to the product of the end bus voltages divided by the characteristic impedance of the line.

**How much electricity is lost in transmission per mile? ›**

So even though electricity may travel much farther on high-voltage transmission lines – dozens or hundreds of miles – losses are low, **around two percent**. And though your electricity may travel a few miles or less on low-voltage distribution lines, losses are high, around four percent.

**What is voltage regulation in short transmission line? ›**

Voltage regulation in transmission lines **occurs due to the impedance of the line between its sending and receiving ends**. Transmission lines intrinsically have some amount of resistance, inductance, and capacitance that all change the voltage continuously along the line.

**What is standard line efficiency? ›**

The line efficiency formula is the number of hours when a high-volume pick-and-place machine is putting parts on the printed circuit board, divided by the number of hours where you are staffing the SMT assembly line. Put more simply, it is **the placement time hours divided by the staffed time hours times 100**.

**Can you use braided line for transmission lines? ›**

A simple answer to this question is absolutely. **Due to the chemical properties of PTFE hose it's a perfect fit for using braided lines for your transmission fluid lines**.

**What is the top most wire transmission lines? ›**

A **guard wire or earth wire** is the topmost conductor in high voltage transmission lines. It is used mainly to protect lines from lightning.

**Why aluminum wire is used for transmission line? ›**

Copper and aluminum are **good conductors of electricity** also they have low resistivity. So they are usually used for electricity transmission.

### Are power transmission lines AC or DC? ›

Typical utility-scale power plants generate alternating current (AC) electricity, and most electrical loads run on AC power. Thus, the majority of transmission lines carrying power around the world are of the **AC type**.

**What is considered a high voltage transmission line? ›**

The electricity supply at home has a voltage of 230 volts (230 V ). However, much higher voltages are used to deliver electricity to homes. **Overhead lines carry up to 380.000 volts (380 kV )** to transport electricity from power stations to towns and urban centres.

**How much power can a 500kV transmission line carry? ›**

A 500kV (500,000 Volt) transmission line carries **1,000 to 1,500 Megawatts** — about 1-1.5 million homes. 500kV is efficient for long-distance bulk energy transmission, similar to a major interstate highway. Typical 500kV structure height: 180-200 feet single pole or lattice towers.

**Can you bury high voltage transmission lines? ›**

Direct buried cables **The traditional means of cable installation for high voltage cables in urban and rural areas is by direct burial**. Trenches approximately 1.5m wide and 1.2m deep are required for each single cable circuit (see indicative diagram on page 12).

**What happens when a transmission line is overloaded? ›**

An overloaded transmission line **may trip, causing power to be redistributed to other transmission lines**, which may get overloaded themselves. This may lead to cascading outages, destabilization, and blackouts.

**Why do you ground transmission lines? ›**

The number one reason for grounding an electrical system is **to cause immediate clearing by providing a path to ground for fault currents**. Maybe people think that grounding stops the flow of electricity, but there is still a flow of current and voltage in a grounded system.

**Why are transmission lines not buried? ›**

First, transmission lines intended for open-air use aren't suitable for burial underground, as **they produce heat that can't dissipate through soil**. For this reason, underground lines must be insulated – adding another step to the process and an additional expense.

**Why do transmission lines fail? ›**

Transmission failures

Transmission failures are much rarer than distribution failures, but when they happen, they can have huge consequences. **Many transmission system failures are caused by weather, but this type of outage can also happen due to equipment failure, computer problems, and human error**.

**What does 100 string efficiency mean? ›**

The greater the string efficiency, the more uniform is the voltage distribution in the each disc insulator. 100% string efficiency implies that **the potential across each disc is same**.

**What is the short transmission line length for 50 Hz? ›**

Short Transmission Line

For the operating frequency of 50 Hz, the length of such a line will be **less than 80 km**.

### What is the length of a long transmission line? ›

A transmission line having a length more than 240 km is consider as a long transmission line. In a long transmission line, parameters are uniformly distributed along the whole length of the line.

**What are the 3 distribution voltages? ›**

Types of AC Distribution System

The commonly used primary distribution voltages are **11 kV, 6.6 kV and 3.3 kV**.

**What are transmission lines also called? ›**

Figure 7-4 Examples of cross sections of uniform transmission lines commonly used as interconnects. As we will see, uniform transmission lines are also called **controlled impedance lines**. There are a great variety of uniform transmission lines, such as twin leads, microstrips, striplines, and coplanar lines.

**What is effective length? ›**

The effective length, L_{E}, of a member hinged at its ends is **the distance between the axes of the hinges**. For general end restraints, the effective length L_{E}, is the length of an end-hinged member which has the same load bearing resistance as the member under consideration.

**What is effective length in mechanics? ›**

The effective length, , is defined by **half the wave length of the curve**. At a distance from an inflection point, the load eccentricity is given by v = v o sin ( π x / L e ) and the moment by M = − EI v ″ = EI v o ( π / L e ) 2 sin ( π x / L e ) .

**What is effective length in engineering? ›**

Effective length is a critical concept in Structural Design which relates to '**the length of a component which is effectively restrained**'.

**What does effective length mean in construction? ›**

Effective length is a critical concept in Structural Design for all structural members such as Steel UC and UB sections, reinforced concrete columns and scaffold tubes. Its technical definition is '**the length of a component which is effectively restrained**'.

**How do you calculate effective length? ›**

The effective length factors of the members are calculated as **K x ≥ 0 for a sway-permitted frame and the out-of-plane effective length factor is specified as K _{y}=1.0**. Each column is considered as nonbraced along its length, and the nonbraced length for each beam member is specified as one-fifth of the span length.

**What is the recommended value of effective length? ›**

What is the recommended value of effective length if the column is effectively held in position and fixed against rotation in both ends? Explanation: Effectively held in position and fixed against rotation in both ends is **0.65 l**. 3.

**How do you calculate the effective length of a pipe? ›**

Complete information about fittings and bends are not generally available at the start of planning a pipeline system. The effective pipe length L is therefore calculated by **multiplying the straight pipe length by 1.6**.

### Why is effective length important? ›

The effective length of a column is important because **it determines the critical buckling load of the column**. A column that is too long or too short for its effective length will not be able to support the required load, which can result in failure.

**What does effective length depend on? ›**

Explanation: Magnitude of effective length depends upon **rotational restraint supplied at end of compression member and upon resistance to lateral movement provided**. 3.

**What is effective length and overall length? ›**

Effective length is the length of a continuous full-size weld. Four times the size of weld. **Effective length is taken as the overall length of the weld minus two times the size of the weld**.

**What is effective length depth? ›**

Effective depth of a beam is **the distance between the centroid of the area of tension reinforcement and the topmost compression fibre**. It is equal to total depth of the beam minus effective cover.

**What is the unsupported length? ›**

Unsupported length is **the clear distance among the member capable of providing lateral support to the column**. For the pin-ended column, it is the distance between the hinges.

**Which of the following is true about effective length? ›**

Which of the following is true about effective length? Explanation: **Effective length shall be taken as length between inner end bolts/rivets of bars for single lacings and 0.7 times length between inner end bolts/rivets of bars for double lacings**.