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## What are transmission loss, dielectric loss, and dielectric loss tangent? Explaining their relationship, calculation methods, and impacts on printed circuit boards (PCB)

HomeSolutionWhat are transmission loss, dielectric loss, and dielectric loss tangent? Explaining their relationship, calculation methods, and impacts on printed circuit boards (PCB)

### What is transmission loss?

Transmission loss refers to signals such as electricity, light, and sound attenuating along the transmission path according to distance. Signal attenuation occurs when a part of the original signal energy is converted into other energy such as heat. The transmission loss on printed circuit boards (PCB) is generally known to increase at higher frequencies.
This article mainly describes what causes transmission loss on printed circuit boards (PCB) as well as how to calculate and reduce this loss.

However, our data introduced later in this article was measured using a printed wired board (PWB), so it is described as PWB. The mechanism and behavior of transmission loss are the same for both PWB and PCB. The definitions of PWB and PCB are as follows.
Printed Wired Board (PWB): A board before components are mounted.
It is a printed board with only wiring before components are mounted. It is sometimes called printed wiring board, raw circuit board, raw board, bare printed circuit board, or bare board.
Printed Circuit Board (PCB): A board after components are mounted.
It is a printed board after components are mounted.

##### Example of transmission loss by frequency Evaluation board: Microstrip line

### Types of transmission loss

Transmission loss has long been calculated and discussed as the sum of dielectric loss and conductor loss. With the transmission loss on printed circuit boards in the high frequency band drawing attention in recent years, the focus has shifted to the difference between measured “transmission loss” and the calculated “sum of dielectric loss and conductor loss”.

Discussions are underway to interpret the difference between these measured and calculated values as the “scattering loss” at dielectric (substrate for PCB) and conductor (signal line) interfaces. While calculation methods have been established for dielectric loss and conductor loss, the method to calculate scattering loss remains under discussion. This article describes the scattering loss in addition to dielectric loss and conductor loss generally viewed as the causes of transmission loss. Transmission loss is defined as the sum of these three losses in this article.

Transmission loss = dielectric loss + conductor loss + scattering loss

#### What is dielectric loss?

Dielectric loss refers to part of the energy being dissipated within a dielectric in the form of heat when an alternating electric field is applied. Dielectric loss depends on the dielectric’s properties, with its magnitude determined by the dielectric loss tangent and permittivity values. The loss generally becomes greater at higher frequencies and as the dielectric loss tangent and permittivity increase.
As for printed circuit boards, conductor signal lines (wiring) are formed on or both on and under the substrates as dielectrics, and when AC signals (current) travel through the signal lines, an alternating electric field is applied to the dielectrics. Some of the signal energy is dissipated within the dielectrics in the form of heat as dielectric loss, resulting in the attenuation of the original signal energy.

##### What is dielectric loss tangent (tan δ, Df, dielectric dissipation factor)?

Dielectric loss tangent refers to the numerical expression of one aspect of the ratio of energy dissipated as heat when an alternating electric field is applied to a dielectric. It is also represented by tan δ, tangent delta, tan delta, dielectric dissipation factor, or dissipation factor, while Df (dielectric dissipation factor) is mainly used in the field of engineering.

When an alternating electric field is applied to an ideal dielectric consisting solely of the capacitive components, the phase difference between the electric field and the current generated by polarization and charge inversion is 90 degrees. As AC power consumption is expressed as the vector product of the electric field and current, a 90-degree phase difference means the power consumption is zero, i.e., no power consumption, no heat, and no loss. However, the phase difference in an actual dielectric deviates from 90 degrees due to the equivalent parallel resistance, which must be assumed in consideration of dielectric polarization and partial discharge, in addition to leakage current that occurs because the resistance of the dielectric itself is finite. If the angle deviation from 90 degrees is δ, then its tangent (tan δ) is equivalent to the component in which the electric field and current are in phase, with only this in-phase component responsible for power consumption, namely, loss. This tangent is referred to as the dielectric loss tangent.

The dielectric loss tangent is a coefficient proportional to the dielectric loss; a larger dielectric loss tangent tan δ, or a larger angle δ deviating from 90 degrees, leads to more power consumption, greater heat generation, and therefore a higher dielectric loss.

The term “electrostatic tangent” is seen in rare cases, but this is believed to be a confusion or mix-up of the “electrostatic capacitance” and “dielectric loss tangent”, which are both basic characteristics in the field of capacitors that is another area apart from printed circuit boards, where dielectric loss tangent is the focus of attention.

##### What are permittivity (ε) and relative permittivity (εr, Dk, k, dielectric constant)?

Permittivity refers to a value expressing the magnitude of a charge generated by polarization in response to a unit electric field applied to a dielectric; it also represents an indicator of how easily the dielectric is polarized. The higher the permittivity, the more charge is generated per the unit electric field, and accordingly, the amount of charge reversing or oscillating positive and negative, or AC current, increases in the applied alternating electric field. Therefore, unless the dielectric loss tangent is zero, higher permittivity causes more power consumption, that is, greater heat generation, leading to higher loss.

In most cases, relative permittivity εr=ε/ε0, which is the ratio of permittivity ε to vacuum permittivity ε0, is often used rather than dielectric permittivity ε itself. The relative permittivity is expressed as Dk (“Dielektrizitätskonstante” in German) primarily in the engineering field, with “k” also used as in “low-k material.” Generally, εr is used in physics, and Dk and k in engineering. The relative permittivity is also represented by relative dielectric constant or dielectric constant.

As described above, the magnitude of dielectric loss is determined by the dielectric loss tangent and permittivity values. Dielectrics (substrate materials for PCB) with a low dielectric loss tangent and low permittivity are required particularly in the high frequency band to reduce the dielectric loss.

#### What is conductor loss?

Conductor loss refers to part of the energy being dissipated as heat (Joule heat) within a conductor due to the resistance and skin effect (details described below) of the conductor used as a signal line (wiring) of printed circuit board. In the case of a constant-current signal, the higher the conductor’s resistance, the more power is consumed, causing higher Joule heat and greater loss. As for an AC signal, higher frequencies contribute to greater loss because the skin effect reduces the skin depth, which is a measure of how far the current travels from the conductor surface, effectively producing higher resistance.

Conductor resistance depends on the conductor’s electrical resistivity, shape, and skin effect, and rises with higher electrical resistivity, narrower, thinner, and longer signal lines, and less skin depth at higher frequencies, thereby increasing the conductor loss.

##### Relationship between conductor loss, skin effect, and resistivity

Skin effect refers to more electric current flowing to the conductor’s outer surface than its center when an alternating electric field is applied. This effect occurs when eddy currents are generated within a conductor with a magnetic field created by electromagnetic induction and induced electromotive force and current produced by the magnetic field. These eddy currents flow in an opposite direction to the current at the center of the conductor, but move in the same direction near the surface; therefore, the skin effect is caused by more current flowing closer to the surface. A measure of how far the current travels from the conductor surface is known as the skin depth. The higher the frequency and the lower the conductor’s electrical resistivity, the more pronounced the skin effect becomes. As the skin effect increases, so does the conductor loss due to less skin depth, which reduces the current's cross-sectional area in effect and increases the conductor’s AC resistance.
As the skin effect increases, it makes less skin depth, which reduces the current’s cross-sectional area in effect and increases the conductor’s AC resistance, so increases the conductor loss.

Conductor resistance can be lowered to reduce the loss, but significantly improving the resistance is considered difficult because copper is almost exclusively used for the conductor’s material from an industrial perspective, electrical resistivity of copper is fixed, magnetic permeability of copper related to electromagnetic induction of the skin effect is fixed, and the shape of the signal lines depends on the design requirements. Other than dielectric loss, scattering loss is now attracting attention as a method to improve transmission loss, as described next.

#### What is scattering loss?

Scattering loss refers to electric signals being scattered and dissipated as heat in the roughened part of conductor surfaces or conductor-substrate interfaces when a high frequency electric field is applied to a conductor.

For printed circuit boards, the conductor surface and interface are usually roughened to enhance the adhesion between signal lines (conductors: copper) and substrates (dielectrics) or other materials. In the past, the impact of this roughening treatment on transmission loss was regarded as a minor problem, but with the skin effect increasing in higher frequency bands, the scattering caused by the roughness of conductor surfaces and conductor-dielectric interfaces has been recognized as a major factor affecting transmission loss. As mentioned at the beginning, this resulting loss is expressed as the difference between measured “transmission loss” and the calculated “sum of dielectric loss and conductor loss”.

There is also the idea that the loss caused by roughened conductor surfaces and interfaces can be viewed as part of the skin effect and included in the conductor loss. This article, however, describes the loss as scattering loss, separate from conductor loss, after determining that it would be easier to understand if the loss resulting from the roughening treatment with its formula under discussion, and the conductor loss that considers the skin depth as increased resistance with its formula already established, are defined as different.

While the scattering loss model and formula have yet to be established amid ongoing discussions, it seems certain that the scattering loss resulting from rough conductor surfaces and conductor-dielectric interfaces through the roughening treatment to enhance adhesion is a major factor. Reducing the scattering loss requires materials capable of minimizing this roughness while ensuring strong adhesion to reduced surface and interface roughness.

### Summary of the differences between dielectric loss, conductor loss, and scattering loss

Dielectric loss A phenomenon in which part of the energy is dissipated as heat within the dielectric when an alternating electric field is applied to a dielectric. Substrate material with both low dielectric loss tangent and low permittivity is required to improve the dielectric loss. A phenomenon in which part of the signal energy is dissipated as heat (Joule heat) within a conductor due to the resistance and skin effect of the conductor used as a signal line (wiring) of the printed circuit board. The conductor’s electrical resistance can be reduced to improve the loss, but the industry’s almost fixed use of copper as a wiring material makes significant improvement difficult. A phenomenon in which electrical signals are scattered and part of the signal energy is dissipated as heat, in the roughened part of conductor surfaces and interfaces. Materials capable of ensuring strong adhesion despite reduced interface roughness are required to improve the scattering loss.

### Calculation methods for transmission loss

#### Formula for dielectric loss

The magnitude of dielectric loss is determined by the dielectric’s permittivity and dielectric loss tangent.

##### Dielectric loss formula αd: Dielectric loss, K: Proportionality constant, f: Frequency, εr: Relative permittivity, tan δ: Dielectric loss tangent

#### Formula for conductor loss

Various conductor loss formulas have been proposed for different circuits. For a simple microstrip line, which is a circuit formed with a signal line of width W on the substrate’s top surface and the ground on the entire bottom surface, conductor loss incorporating the skin effect is expressed in the following formula.

##### Conductor loss formula αc: Conductor loss, K1, K2, K3: Proportionality constants, f: Frequency, ρ: Resistivity, W: Line width, R: Resistance of conductor,
d: Skin depth, μ: Magnetic permeability

For details of calculating a microstrip line (MSL) and coplanar waveguide (CPW), please refer to the following references introducing the major formulas.

MSL:
Cam Nguyen, “Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures,” JOHN WILEY & SONS, INC., 2000, p. 68-71.

CPW and CPW with back conductors:
K. C. Gupta, R. Garg, I. J. Bahl, “Microstrip Lines and Slotlines,” Artech House, 1979.
Cam Nguyen, “Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures,” JOHN WILEY & SONS, INC., 2000, p. 71-74.

#### Discussions on the formula for scattering loss

Scattering loss models have been proposed up to this point (September 2021) due to the dielectric loss and conductor loss formulas alone failing to match the measured values, but discussions are ongoing over the accuracy of the scattering loss formula. Please refer to the following references for the major scattering loss calculation models.

Paul G. Huray, “The Foundations of Signal Integrity,” IEEE PRESS, John Wiley & Sons, Inc., 2010, p. 216-276.
Stephen C. Thierauf, “High-Speed Circuit Board Signal Integrity,” ARTECH HOUSE, INC., 2004, p. 17-30.

For the time being, it seems realistic to understand the difference between measured “transmission loss” and the calculated “sum of dielectric loss and conductor loss” as “scattering loss”.

### What is transmission loss on printed circuit boards (PCB)? (Summary so far)

Transmission loss generated in signal lines on a printed circuit board is expressed as the sum of the dielectric loss determined by the dielectric loss tangent and permittivity of a dielectric used as a substrate material for PCB, the conductor loss caused by the resistance of a conductor used as a signal line of PCB, and the scattering loss resulting from the roughness of signal line surfaces and signal line-substrate interfaces.

Transmission loss = dielectric loss + conductor loss + scattering loss

### Examples and impact of transmission loss on printed circuit boards (PCB)

#### Example 1: Dielectric loss

Dielectric loss is determined by the dielectric loss tangent and permittivity of a dielectric used as substrate material of the printed circuit board, and the loss increases at higher frequencies.

The following are the measurement results using Showa Denko Materials’ printed wired boards (PWB). The transmission losses vary due to the variation of dielectric loss with different dielectric loss tangent and permittivity values.

##### Example of transmission losses varying due to the variation of dielectric loss with different dielectric loss tangent and permittivity values Evaluation board: Microstrip line
Characteristic impedance: Approx. 50 Ω
Calibration method: TRL
Temperature and humidity: 25 ℃/60 %RH

Item

Condition

Product A

Product B

Product C

Permittivity*

10 GHz

3.07

2.97

2.95

Dielectric loss tangent*

10 GHz

0.0021

0.0015

0.0013

*Based on the cavity resonator perturbation method.

#### Example 2: Scattering loss

The surface of a conductor (copper) used for a signal line of a printed circuit board is generally roughened to enhance adhesion to various materials. However, the effect of the roughened part of surfaces and interfaces becomes larger, due to the skin effect increasing and the skin depth decreasing in higher frequency. Scattering loss refers to the signal in this roughened part being scattered and dissipated as heat. This loss, related to the roughness of the conductor surface, becomes greater with rougher surfaces.

### Showa Denko Group’s solutions

Dielectric loss positively correlates with the dielectric loss tangent and permittivity of substrate materials and resins. More precisely, dielectric loss is proportional to the dielectric loss tangent and the square root of permittivity. We therefore believe the dielectric loss tangent and permittivity of substrate materials and resins as dielectrics must be lowered to reduce the dielectric loss. In addition, given that the scattering loss can be reduced by decreasing conductor surface and interface roughness, we also believe it is necessary to improve substrate materials capable of ensuring adhesiveness with reduced surface roughness and resins or adhesive sheets with improved adhesion strength.

Showa Denko Materials offers a variety of substrate materials and resins with superior low dielectric properties and adhesion strength. Transmission loss can be reduced by using well-balanced low dielectric resins.