1. The PCB transmission line consists of at least two wires—one for the signal and the other for the return path. This basic structure underpins more complex circuit board nets. From a PCB design perspective, understanding these structures (microstrip, stripline, and coplanar) is crucial for both designers and manufacturers.
2. What is the loss of the transmission line?
3. Transmission lines exhibit various loss mechanisms. The total loss of a PCB transmission line, known as insertion loss (αt), is the sum of conductor loss (αc), dielectric loss (αd), radiation loss (αr), and leakage loss (αl).
4. αt = αc + αd + αr + αl
5. Leakage loss is minimal due to the high volume resistance of PCBs. Radiation loss represents energy lost through radio frequency radiation and is influenced by frequency, dielectric constant (Dk), and thickness. For a given transmission line, higher frequencies result in greater loss. Additionally, a thinner substrate and higher Dk value reduce radiation loss.
6. This article will focus on the transmission line loss related to conductor loss (αc) from signal trace resistance and dielectric loss (αd) from the PCB dielectric, the latter measured by the loss tangent or dissipation factor.
**αt = αc + αd**
**Characteristic impedance and loss mechanism**
In our previous PCB transmission line series, we provided the characteristic impedance of a transmission line (which is the impedance seen by the signal and is independent of frequency):
**R = line conductor resistance per unit length (pul)**
**L = the inductance of the line conductor loop pul**
**G = conductance between signal path and return path (due to dielectric) pul**
**C = the capacitance pul between the signal path and the return path (it increases with the Dk of the dielectric)**
For a uniform transmission line, R, L, G, and C are consistent throughout, so Zc remains constant along the transmission line.
For a sinusoidal signal with a frequency of f (ω = 2πf) propagating along the line, the voltage and current expressions at different points and times are given by:
Where α and β are the real and imaginary parts of the PCB transmission line loss, expressed by the following formula:
At the frequencies of interest, R << ωL and G << ωC, thus:
And: the loss of the PCB transmission line is:
This implies that a wave propagates with a loss per unit length and attenuates as it travels along the line.
The signal attenuation coefficient for a transmission line of length l is:
The attenuation or signal loss factor is typically expressed in dB.
Therefore, dB loss is proportional to the line length. We can thus express the above as dB loss per unit length:
We usually omit the minus sign, keeping in mind that it represents dB loss, which is always subtracted from the signal strength in dB.
The above is also referred to as the total insertion loss per unit length of the transmission line, denoted as:
Now, the R/Z0 component of loss is proportional to R (resistance per unit length), known as conductor loss, caused by the resistance of the conductor forming the transmission line. It is represented by αc. The loss of the GZ0 part is proportional to G—the conductance of the dielectric material, termed dielectric loss, and denoted by αd.
Where R is the resistance of the conductor per inch.
There are two conductors in the PCB transmission line—the signal trace and the return path.
Usually, the return path is a flat surface; however, the return current is not evenly distributed across this surface. It can be shown that most of the current concentrates on a strip three times the width of the signal trace, just below the signal trace.
**Signal trace resistance in PCB transmission lines**
Does the entire cross-sectional area of the signal trace participate equally in the signal current? The answer is: not always—it depends on the signal frequency.
At very low frequencies—up to about 1 MHz—we assume the entire conductor participates in the signal current, so Rsig equals the αc resistance of the signal trace, i.e.:
**ρ = Copper resistivity in ohms-inch**
**W = trace width in inches (e.g., 5 mils or 0.005″ trace 50 ohms)**
**T = trace thickness in inches (typically ½ oz to 10 oz, i.e., 0.0007″ to 0.0014″)**
For example, for a 5 mil wide trace:
For our purposes, we are interested in AC resistance at frequency f. Here, the skin effect becomes relevant. According to the skin effect, current at frequency f penetrates only to a certain depth, known as the skin depth of the conductor.
We see that at 4 MHz, the skin depth is equivalent to 1 oz of copper thickness, and at 15 MHz, it is equivalent to ½ oz of copper thickness. Above 15 MHz, the signal current depth is less than 0.7 mils and continues to decrease as the frequency increases.
Since we focus on high-frequency behavior, we assume that T exceeds the skin depth at the frequency of interest, so we use skin depth instead of T in the signal resistance formula. Therefore:
We use 2δ instead of δ, as the current utilizes the entire periphery of the conductor—technically, 2W can be replaced by 2(W+T).
The return signal propagates only with a thickness δ along the surface closest to the signal trace, and its resistance can be approximated as:
**Increased conductor loss due to copper surface roughness at the conductor-dielectric interface**
It is crucial to know that the “copper conductor-dielectric interface” on the circuit board is never smooth (a smooth interface would cause the copper conductor to peel from the dielectric surface). Instead, it is roughened into a tooth-like structure to enhance the peel strength of the conductor on the board.
2. What is the loss of the transmission line?
3. Transmission lines exhibit various loss mechanisms. The total loss of a PCB transmission line, known as insertion loss (αt), is the sum of conductor loss (αc), dielectric loss (αd), radiation loss (αr), and leakage loss (αl).
4. αt = αc + αd + αr + αl
5. Leakage loss is minimal due to the high volume resistance of PCBs. Radiation loss represents energy lost through radio frequency radiation and is influenced by frequency, dielectric constant (Dk), and thickness. For a given transmission line, higher frequencies result in greater loss. Additionally, a thinner substrate and higher Dk value reduce radiation loss.
6. This article will focus on the transmission line loss related to conductor loss (αc) from signal trace resistance and dielectric loss (αd) from the PCB dielectric, the latter measured by the loss tangent or dissipation factor.
**αt = αc + αd**
**Characteristic impedance and loss mechanism**
In our previous PCB transmission line series, we provided the characteristic impedance of a transmission line (which is the impedance seen by the signal and is independent of frequency):
**R = line conductor resistance per unit length (pul)**
**L = the inductance of the line conductor loop pul**
**G = conductance between signal path and return path (due to dielectric) pul**
**C = the capacitance pul between the signal path and the return path (it increases with the Dk of the dielectric)**
For a uniform transmission line, R, L, G, and C are consistent throughout, so Zc remains constant along the transmission line.
For a sinusoidal signal with a frequency of f (ω = 2πf) propagating along the line, the voltage and current expressions at different points and times are given by:
Where α and β are the real and imaginary parts of the PCB transmission line loss, expressed by the following formula:
At the frequencies of interest, R << ωL and G << ωC, thus:
And: the loss of the PCB transmission line is:
This implies that a wave propagates with a loss per unit length and attenuates as it travels along the line.
The signal attenuation coefficient for a transmission line of length l is:
The attenuation or signal loss factor is typically expressed in dB.
Therefore, dB loss is proportional to the line length. We can thus express the above as dB loss per unit length:
We usually omit the minus sign, keeping in mind that it represents dB loss, which is always subtracted from the signal strength in dB.
The above is also referred to as the total insertion loss per unit length of the transmission line, denoted as:
Now, the R/Z0 component of loss is proportional to R (resistance per unit length), known as conductor loss, caused by the resistance of the conductor forming the transmission line. It is represented by αc. The loss of the GZ0 part is proportional to G—the conductance of the dielectric material, termed dielectric loss, and denoted by αd.
Where R is the resistance of the conductor per inch.
There are two conductors in the PCB transmission line—the signal trace and the return path.
Usually, the return path is a flat surface; however, the return current is not evenly distributed across this surface. It can be shown that most of the current concentrates on a strip three times the width of the signal trace, just below the signal trace.
**Signal trace resistance in PCB transmission lines**
Does the entire cross-sectional area of the signal trace participate equally in the signal current? The answer is: not always—it depends on the signal frequency.
At very low frequencies—up to about 1 MHz—we assume the entire conductor participates in the signal current, so Rsig equals the αc resistance of the signal trace, i.e.:
**ρ = Copper resistivity in ohms-inch**
**W = trace width in inches (e.g., 5 mils or 0.005″ trace 50 ohms)**
**T = trace thickness in inches (typically ½ oz to 10 oz, i.e., 0.0007″ to 0.0014″)**
For example, for a 5 mil wide trace:
For our purposes, we are interested in AC resistance at frequency f. Here, the skin effect becomes relevant. According to the skin effect, current at frequency f penetrates only to a certain depth, known as the skin depth of the conductor.
We see that at 4 MHz, the skin depth is equivalent to 1 oz of copper thickness, and at 15 MHz, it is equivalent to ½ oz of copper thickness. Above 15 MHz, the signal current depth is less than 0.7 mils and continues to decrease as the frequency increases.
Since we focus on high-frequency behavior, we assume that T exceeds the skin depth at the frequency of interest, so we use skin depth instead of T in the signal resistance formula. Therefore:
We use 2δ instead of δ, as the current utilizes the entire periphery of the conductor—technically, 2W can be replaced by 2(W+T).
The return signal propagates only with a thickness δ along the surface closest to the signal trace, and its resistance can be approximated as:
**Increased conductor loss due to copper surface roughness at the conductor-dielectric interface**
It is crucial to know that the “copper conductor-dielectric interface” on the circuit board is never smooth (a smooth interface would cause the copper conductor to peel from the dielectric surface). Instead, it is roughened into a tooth-like structure to enhance the peel strength of the conductor on the board.
