# Twisted Pair Impedance Calculator

 Impedance Ohms (Ω) Delay ns/in Inductance nH/in Capacitance pF/in

## Twisted pair cables

You can create an electrical signal transmission line using two conductors. Twisted-pair (TP) cables are known to make the most effective signal transmission lines. A twisted-pair cable simply consists of two insulated wires twisted together. Normally, a pair of 22 to 26-gauge copper wires with an insulating protective layer are used to make a twisted pair wire.

In actual use, multiple twisted pairs are wrapped up in an insulating sleeve to form a twisted pair cable. But in daily life, the term “twisted pair cable” directly refers to the “twisted pair wire”. When several twisted pairs are combined, they form multi-pair twisted cables. The individual conductors in multi-pair cables are twisted into pairs that have varying twists to reduce crosstalk. In such cases, specific color combinations are used for pair identification.

In a twisted-pair cable, the insulated copper wires are twisted together at a particular density, such that the radio waves radiated by the first conductor during signal transmission are offset by the radio waves emitted by the second conductor. This effectively reduces the degree of signal interference. For this reason, twisted pairs are mainly used with balanced signals, as they readily reduce radiated Electromagnetic Interference (EMI) and are able to mitigate the effects of received EMI.

Generally, twisted pair cables are the most preferred form of transmission media in integrated electrical wiring projects. This is because electrical signal transmission lines are highly likely to create large return path loops if they are not connected properly. But twisted-pair cables ensure that the return path is as close to the signal being transmitted as possible, this helps maintain a constant impedance as more uniform capacitance and inductance values are created per unit length of the transmission line.

Note, compared to other transmission media, twisted-pair cables are subject to various restrictions in terms of data transmission speed, channel width, and transmission distance; though their prices are relatively low.

## Applications of Twisted-Pair Cables

• Twisted-pair cables are widely used for telecommunication and data communication applications in structured cabling systems. They are especially valuable if used with two electrical signals that are transmitting information differentially, i.e., using the negative and positive versions of the same electrical signal. A differential system is also referred to as a balanced system since the negative and positive signals are “balanced” on both sides of the common-mode voltage. In such a system, the differential receiver minuses the negative signal from the positive signal, so any voltage components present in the two signals are eliminated.
• The close physical proximity of the two copper wires in the twisted pair ensures that external EMI (Electromagnetic Interference) will be coupled almost equally into both conductors. This in turn makes sure that the differential receiver circuitry eliminates any EMI-related electrical noise. That’s why balanced signal systems are more robust against electrical noise- as long as the noise is occurring in both signals.
• Twisted-pair cables help to reduce crosstalk on multi-pair cables and noise pickup from external sources. Also, cable twisting plays a key role in minimizing the generation of EMI. This is because differential signals generate EMI with opposing polarity, so the generated EMI is largely canceled. The EMI-canceling is more pronounced when two conductors in a twisted pair are in close proximity. The advantages of improved ground bounce, low signal-to-noise ratio, and reduced crosstalk which balance signal transmission are particularly valuable in stereo(high-fidelity) and wide bandwidth systems.
• Twisted-pair cables are useful even without shielding. By transmitting electrical signals along with a 180o out-of-phase complement, ground and emissions currents are theoretically canceled out. This results in improved EMI performance, as well as reduced grounding and shielding requirements for twisted-pair transmission compared to single-ended transmission.
• The most typical form of twisted pair cables is the Unshielded Twisted Pair (UTP). UTP cables consist of just two copper wires with an insulating protective layer that are twisted together. They are mainly used in normal telephone cables and any data communication cables. Nevertheless, Shielded Twisted-Pair (STP) cables can provide further circuitry protection against EMI. The STP cables differ from UTP cables in that they have a foil jacket that helps them counter external electrical noise and crosstalk.
• Also, there is a special type of twisted-pair cable used in data communications known as the Foil Shielded Pair (FTP) cable. The FTP cable incorporates four twisted pairs inside a common shield which is made of aluminum foil.

## What is Twisted Pair Impedance?

Impedance is simply defined as the opposition to the flow of alternating current (AC) within an electric circuit. It can be said to be a more general term for resistance that also includes reactance (combination of both inductance and capacitance). Thus, while resistance in an electric circuit occurs due to the contribution of a resistive element only. Impedance occurs because of the presence of three components, namely resistance, capacitance, and inductance; all of which oppose current flow in an AC circuit. Hence, impedance is the combination of both reactance and resistance in an electric circuit. Also, resistance occurs in both DC and AC circuits, whereas, impedance is only present in AC circuits.

Often, you’ll come across the word ‘impedance’ in electrical signal transmission lines, like the cables that run between the components of your stereo system. It is an important factor that is considered in the design and analysis of AC circuits. Also, when you’re purchasing an electronic device, you might be advised to match the impedance of the cables, or else you’ll get a reflection. This is where twisted-pair impedance comes into play, often referred to as the characteristic impedance of a twisted-pair cable.

When the two insulated copper wires are twisted together over the length of a cable at a constant twisting rate, the result will be a twisted-pair cable with a well-defined characteristic impedance. Characteristic impedance (denoted as Z0) of a twisted pair is determined by the spacing and the size of the conductors (copper wires), and the type of dielectric used between the two wires. Hence, a balanced twisted pair has a Z0 (characteristic impedance) that depends on the ratio of the copper wire spacing to the wire diameter. So, the geometries of the twisted pair that you should pay close attention to, are the diameter of the conductive wire(D) and the center-to-center distance between the two conductors(S), as shown in the diagram to the right.

The effective permittivity of the dielectric material between the two conductors (copper wires) has a value that lies between the relative permittivity of air and the permittivity of the insulation on the copper wires. In practical twisted pair transmission lines, characteristic impedance(Z0) at high frequencies is very similar to pure resistance, but not exactly.  This can be explained by the fact that the impedance of a twisted-pair cable is a function of the spacing between the two copper wires, so separating the two wires significantly changes the characteristic cable impedance at that point.

It is important that you determine the characteristic impedance of a given twisted-pair cable, as this impedance must match the impedance of the receiving and transmitting circuitry. This article will help you understand how you can determine the characteristic impedance using a twisted-pair impedance calculator.

## How is Cable Impedance Calculated?

Impedance is measured in Ohms (Ω) and is represented by the symbol Z. As previously stated, there are two different components that contribute to the impedance of any electric circuit. These are:

• Resistance (R): This is the opposition to current flow due to the effects of the shape and material of a component. The effect is more pronounced in resistors, but all components have some sort of resistance to current flow.
• Reactance (X): This is the opposition to current flow due to the presence of magnetic and electric fields that oppose changes in circuit voltage or current. Reactance is mostly notable in inductors and capacitors.

Also, impedance is a complex number that consists of real and imaginary values. It is expressed mathematically as:

Z = R + jX ……… (1.1)

From the formula above, the real part of the impedance equation is Resistance (R), while the imaginary part is (jX)– the reactance. j is the imaginary number √ (-1). Reactance (X) can either be Inductive reactance expressed as: XL = 2πfL = ωL, or Capacitive reactance given by: XC = 1 / (2πfC) = 1 / (ωC). But in most cases, Reactance (X) is a combination of both Inductive reactance (XL) and Capacitive reactance (XC).

Note, in the equations for both Inductance and Capacitance reactance f = frequency (Hz)which shows that Impedance varies according to the working frequency of the circuit or rather the frequency of the AC currentL is the measured inductance; C is the measured capacitance of a particular circuit. Inductance is measured in Henrys, while capacitance is measured in Farads. Also, in the two equations, 𝜔 is the angular frequency (2 × 𝜋 × f). Therefore, the amount of opposition to current flow by inductors and capacitors in a circuit varies depending on how the AC current changes in speed, strength, and direction. That’s why impedance has both magnitude and phase angle.

Therefore, to calculate the magnitude of impedance for any electric circuit, you must know the value of all resistors and the reactance of all capacitors and inductors in the circuit. Hence, Eq. (1.1) can be expressed as:

Z = √(R2 + X2T

Z = √[R2 + (XL − XC)2]………(1.2)

θ = arctan⁡ (XT / R

where,

Z = magnitude of impedance in Ω (ohms) in a series circuit

XT = total reactance in Ω (ohms) = XL – XC

θ = the phase angle of impedance (in degrees)

In a general series circuit, you cannot just add the values of reactance and resistance together, as the two values always are “out of phase”. This means that the two values change over time as part of the Alternating Current cycle, but they attain peak values at different times. So, for a series connection the value of impedance is obtained using this formula:

Z = √[R2 + (XL – XC)2] or Z = √(R2 + X2T)

On the other hand, in a general parallel circuit that includes both reactance and resistance, the total impedance can only be calculated in terms of complex numbers. This is possible by using the formula in Eq. (1.1): Z = R + jX. For example, the impedance of a certain AC circuit with resistance and reactance in a parallel configuration can be expressed as: Z = 60Ω + j140Ω. In case you have two such like circuits connected in series, then you can separately add the imaginary and real components together. For instance, if a parallel circuit Z1 = 80Ω + j120Ω is connected in series to a resistor Z2 = 30Ω; then, the total impedance of the entire circuit will be: Ztotal = 110Ω + j120Ω.

## Calculating the Characteristic Impedance of a Twisted Pair

Characteristic impedance or surge impedance is defined as the ratio of voltage amplitude to current amplitude for a signal that is propagating in a single direction on a uniform transmission line; without the signal being reflected in other directions. It is a very important parameter in the design and analysis of systems using electrical signal transmission lines, including those made of twisted-pairs.

The twisted pair characteristic impedance (Z0) is the impedance that an electrical signal will experience as it travels through the length of a twisted-pair cable. This type of impedance depends on the following twisted-pair characteristic properties:

• Propagation Delay (delay): This is the time a signal takes to travel through a specific distance.
• Inductance Per Unit Length (𝑳𝒕𝒘𝒊𝒔𝒕𝒆𝒅 𝒑𝒂𝒊𝒓): It is important to know the inductance of the signal being transmitted. Especially when creating models for twisted pair transmission lines using simulation tools.
• Capacitance Per Unit Length (𝑪𝒕𝒘𝒊𝒔𝒕𝒆𝒅 𝒑𝒂𝒊𝒓): When designing twisted pair transmission line models using simulation tools, it is important that you know the capacitance of the signal being transmitted.

As previously mentioned, twisted pair Characteristic Impedance (Z0) is influenced by the spacing between the conductors and the size of the copper wires (diameter of the conductors), and the type of dielectric used between the two wires. It can be expressed mathematically as:

Z0(twisted pair) = [120 / √er] × ln[2S / D]………(2.1)

where,

er = the effective substrate dielectric (of the material between the conductors)

D = the diameter of the conductor (the copper wire), as shown in Figure 1.

S = the spacing between the two insulated copper wires that make up the twisted pair, as shown in Figure 1.

The other characteristic properties of a twisted pair can be obtained mathematically using the following formula:

delay = 84.72 × 10−3 × √er

Ltwisted pair = 10.16 × 10−9 × ln[2S / D]

Ctwisted pair = {0.7065 / [ln⁡ (2S / D)]} × er

## Twisted Pair Impedance Calculator

This is a tool that has been designed to determine the characteristic impedance (Z0) of a twisted-pair cable. As you can see, calculating the twisted pair characteristic impedance by hand using Eq. (2.1) isn’t overly complicated. However, it will definitely take longer compared to using a calculator. Also, approximating the other characteristic properties of twisted-pair transmission lines at the design stage can be tedious and ineffective if done through hand calculations. Because designing a transmission line means you keep manipulating the characteristic properties of a twisted pair, to see which values will give the best results.

The Twisted Pair Impedance Calculator is able to compute the characteristic impedance Z0(twisted pair) based on the dimensions of the twisted-pair cable. Moreover, this tool can also compute the signal propagation delay in inches per nanosecond (ns/in), the inductance per unit length in nano-Henrys per inch (nH/in), and the capacitance per unit length in pico-Farads per inch (pF/in). Thus, with this calculator you can get immediate results for all the aforementioned characteristic properties of a twisted-pair cable with no effort.

The only values you’ll need to know before using such a calculator are: (i) Diameter (D) of the copper wires used, normally referred to as the internal diameter of the conductor. D can be measured in centimeters (cm), millimeters (mm), micrometers (µm), mils (mil), or inches (in). (ii) The separation (S) between the two copper wires that make up the twisted pair, also referred to as the spacing between the conductors. S can be measured in millimeters (mm), centimeters (cm), mils (mil), micrometers (µm), or inches (in). (iii) Substrate dielectric, er is the relative dielectric permittivity; which is a dimensionless number.

You can then enter the three values in the input fields provided on the calculator. And on clicking the “Calculate” button, the calculator will automatically output: the characteristic impedance (Z0) of the twisted pair in Ω(Ohms), the signal Propagation Delay in (ns/in), Inductance per inch in (nH/in), and Capacitance per inch in (pF/in); as illustrated in Figure 3.

Note, the values of D and S that you’ll input to the twisted pair impedance calculator must have the same dimensions so that the calculator can output the correct values with standard units. Also, the calculator rounds off the output values to the second decimal place.