## 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 modelled 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

## Measuring balun common mode impedance – #3

A correspondent having read my series Measuring balun common mode impedance – #1 related difficulties with his Rigexpert AA-230Zoom.

The articles showed some techniques for measuring common mode impedance of a current balun.

The following examples are of a test choke wound on a BN43-202 binocular core, and the results are quite similar to what might be expected of a broadband HF current balun. The measurements were made with a Rigexpert AA-600. Above, the measurement result using RigExpert’s newest software Antscope2. Continue reading Measuring balun common mode impedance – #3

## Small common mode choke for analyser antenna measurements using 2843000202 (BN43-202)

The project is design, implementation and test of a small common mode choke for use with an analyser for antenna measurements.

The choke must have medium to high Zcm from 1 to 30MHz. It is intended to be used with analysers supporting SOL calibration, so effectively any impedance transformation within the fixture is compensated and the reference plane is the load side terminals of the device.

The candidate core is a low cost #43 binocular ferrite core that is fairly easy to obtain. Above is a first pass check of the likely Zcm at 1.8MHz using a Fair-rite 2843000202 (BN43-202) binocular core. These chokes have relatively low self resonance frequency so a value for Cs is supplied that delivers self resonance at around 5MHz. Zcm at 1.8MHz needs 8-9t, 8.5t will be used (ie the twisted pair enters one end of the binocular and leaves the other end for convenient layout). (8.5t is not strictly correct, but it is a close approximation in this case.)
Continue reading Small common mode choke for analyser antenna measurements using 2843000202 (BN43-202)

## Equivalent noise bandwidth – IC-7300 CW Rx Filter2 – (500Hz sharp)

For a lot of experiments, knowledge of the Equivalent Noise Bandwidth (ENB) of a receiver is necessary. The ENB is the bandwidth of an ideal rectangular filter with the same gain as some reference frequency.

Though filters are often specified in terms of bandwidth at x dB down, that metric is of relatively little value, the x is often 6dB but not always, the filters depart significantly from ideal or even common response.

In brief, a white noise source is connected to the receiver input, Filter2 (nominal 500Hz bandwidth sharp response) selected and set to standard PBT, and the audio output captured on a PC based audio spectrum analyser, Spectrogram 16 in this case.

Spectrogram is set to integrate over 30s to average the variations due to the noise excitation. The resulting graph and text spectrum log are saved.

The method is explained in detail at Measure IF Bandwidth. Above is the spectrum plots, as receivers go this is relatively flat.
Continue reading Equivalent noise bandwidth – IC-7300 CW Rx Filter2 – (500Hz sharp)

## Equivalent noise bandwidth – IC-7300 SSB Rx Filter2 – (2400Hz sharp)

For a lot of experiments, knowledge of the Equivalent Noise Bandwidth (ENB) of a receiver is necessary. The ENB is the bandwidth of an ideal rectangular filter with the same gain as some reference frequency, 1kHz is usually specified for SSB telephony receiver sensitivity measurement.

Though filters are often specified in terms of bandwidth at x dB down, that metric is of relatively little value, the x is often 6dB but not always, the filters depart significantly from ideal or even common response.

In brief, a white noise source is connected to the receiver input, Filter2 (nominal 2400Hz bandwidth sharp response) selected and set to standard PBT, and the audio output captured on a PC based audio spectrum analyser, Spectrogram 16 in this case.

Spectrogram is set to integrate over 30s to average the variations due to the noise excitation. The resulting graph and text spectrum log are saved.

The method is explained in detail at Measure IF Bandwidth. Above is the spectrum plots, as receivers go this is relatively flat, lacking the usual tapering off above 1kHz (a technique to cheat on sensitivity specs).
Continue reading Equivalent noise bandwidth – IC-7300 SSB Rx Filter2 – (2400Hz sharp)

## DSZH WK-6889 – temperature sensor

The specifications of the DSZH WK-6889 – temperature sensor do not give accuracy or type of the temperature sensors used. They are most likely to be one of: RTD, thermocouple, or NTC thermistor. Continue reading DSZH WK-6889 – temperature sensor