Do Distortionless Lines exist?

I am asked about my use of the term Distortionless Lines from time to time, often in the vein of they don’t exist, so why discuss them?

Concept

The concept derives from the work of Heaviside and others in seeking a solution to distortion in long telegraph lines.

The problem was that digital telegraph pulses were distorted due to different attenuation and propagation time for different components of the square waves.

Heaviside proposed that transmission lines could be modelled as distributed resistance (R), inductance (L), conductance (G) and capacitance (C) elements.

In each incremental length Δx, there is incremental R, L, G and C. Continue reading Do Distortionless Lines exist?

Transmission lines: departure from ideal Zo

The article On the concept of that P=Pfwd-Prev discussed the question of the validity of the concept of that P=Pfwd-Prev, exploring an example of a common nominally 50Ω coaxial cable at 100kHz. The relatively low frequency was used to accentuate the departure from ideal.

This article digs a little further with analyses at both 100kHz and 10MHz.

100kHz

A plot was given of the components and sum of terms of the expression for power at a point along the line.

Lets look at the power calculated from voltages and currents for the example at 100kHz where Zo=50.71-j8.35Ω and Zload=5+j50Ω.

Above, the four component terms are plotted along with the sum of the terms. Continue reading Transmission lines: departure from ideal Zo

From lossless transmission line to practical – Zo and γ

On the concept of that P=Pfwd-Prev discussed the expression for power at a point on a line in terms of the travelling wave voltage and current components.

The expansion of P=real((Vf+Vr)*conjugate(If+Ir)) gives rise to four terms.

This article looks at the components of that expansion for a mismatched line for a range of scenarios.

The scenarios

  • Lossless Line;
  • Distortionless Line; and
  • practical line.

We will override the imaginary part of Zo and the real part of γ (the complex propagation coefficient) to create those scenarios. The practical line is nominally 50Ω and has a load of 10+j0Ω, and models are at 100kHz.

Lossless Line

A Lossless Line is a special case of a Distortionless Line, we will deal with it first.

A Lossless Line has imaginary part of Zo equal to zero and the real part of γ equal to zero.

Above is a plot of the four components of power and their sum at distances along the line (+ve towards the load). Continue reading From lossless transmission line to practical – Zo and γ

SimSmith example of VSWR assessment

A reader of On the concept of that P=Pfwd-Prev asked if / how the scenario discussed could be modeled in SimSmith.

SimSmith uses different transmission line modelling to what was used in that article, but a SimSmith model of RG58A/U allows illustration of the principles and it will deliver similar results.

Let’s explore the voltage maximum and minimum nearest the load to show that VSWR calculated from the magnitude of reflection coefficient is pretty meaningless in this scenario.

Above is the basic model. I have created two line sections, one from the load to the first voltage maximum, and another to the first voltage minimum where I have placed the source. I have set Zo to the actual Zo of the line as calculated by SimSmith (56.952373-j8.8572664Ω), effZ as SimSmith calls it, so the Smith chart relates to the real transmission line. Continue reading SimSmith example of VSWR assessment

On the concept of that P=Pfwd-Prev

The article On negative VSWR – Return Loss implications raised the question of the validity of the concept of that P=Pfwd-Prev.

The Superposition Theorem is an important tool in linear circuit analysis, and is used to find the combined response of independent sources. Superposition applies to voltages and currents, but not power. Continue reading On the concept of that P=Pfwd-Prev

On negative VSWR – Return Loss implications

On negative VSWR (read it first) discussed the case of negative VSWR results from some calculating tools  and formulas, and more generally that simple formulas that depend on lossless line assumptions produce errors on practical lossy line scenarios.

Return Loss is defined as the ratio Pfwd/Prev, often given in dB.

Return Loss is usually calculated as 20*log(1/ρ), it yields negative calculated Return Loss for ρ>1. It would be a mistake to doctor the result to hide the negative return loss as it is a strong hint that the results may be invalid.

An important consideration here is the validity of the concept of Pfwd and Prev. Continue reading On negative VSWR – Return Loss implications

On negative VSWR – a worked example

On negative VSWR (read it first) discussed the case of negative VSWR results from some calculating tools  and formulas, and more generally that simple formulas that depend on lossless line assumptions produce errors on practical lossy line scenarios.

This article exposes an example at 100kHz where Zo=50.71-j8.35Ω and Zload=5+j50Ω.

If we were to use a probe to directly measure the magnitude of line voltage, we would expect the following.

Above, the standing wave plot. At first appearance it might look like a classic standing wave plot, but it is not… there is a tiny difference in the shape at the right hand side. Continue reading On negative VSWR – a worked example

On negative VSWR

Some calculating tools come up with a negative value of VSWR under some circumstances.

Considering the meaning of VSWR: the ratio of the voltage maximum on a long transmission line to the adjacent voltage minimum, calculated negative VSWR might seem an aberration, invalid even. Note that nothing in this definition makes VSWR a property of a dimensionless point on a line.

VSWR can be measured directly by sampling voltage along a transmission line with a voltage probe. That said, it is almost never done and VSWR is inferred from other measurements, usually point measurements.

A transmission line is free to carry waves in two directions, and the ratio of voltage to current for each of those waves is the characteristic impedance Zo. Continue reading On negative VSWR

The private and public scope of coaxial cable

Let’s start by reviewing the concept of inductance.

Inductance

Inductance of a conductor is the property that a change in current in a conductor causes a electro motive force (emf or voltage) to be induced in a conductor.

We can speak of self inductance where the voltage is induced in the same conductor as the changing current, or mutual inductance where the changing current in one conductor induces a voltage in another conductor. Continue reading The private and public scope of coaxial cable