Some recent articles discussed some effects that in part are a result of Zo having a complex value (ie a non-zero imaginary part). Continue reading On working with complex Zo

# Category: Amateur Radio

## 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

## Average power of SSB telephony – experimental verification

Average power of SSB telephony used 80 year old research by (Holbrook and Dixon 1939) to come up with a ratio of peak voltage to RMS voltage of a voice waveform, and from that derive the ratio PEP/Pav..

(Holbrook and Dixon 1939) explored the subject measuring the voice characteristics of many talkers (as there is variation amongst talkers) to come up with an average characteristic.

Whilst in its day, obtaining instantaneous samples of voice was a challenge, it is trivial today and if you can’t believe the numbers given, try your own experiment (but realise it is for your own voice rather than the general population).

Many modern PC sound applications are capable of the measurement, I will demonstrate it with the feed Windows application Audacity with the stats.ny addin.

Above is a screenshot of a 6s recording of my voice made without stopping for breath. The statistics window shows a peak of -8.9dBFS and RMS of -27.4dBFS, giving a peak voltage to RMS voltage ratio of 18.5dB. Continue reading Average power of SSB telephony – experimental verification

## Power rating of a ferrite cored transformer or balun

Commercial products often have power ratings that bear checking.

There are common some key properties that are relevant:

- where loss is high, core loss tends to dominate;
- the specific heat of ferrite is typically quite high;
- the capacity to dissipate heat is related to many factors.

Continue reading Power rating of a ferrite cored transformer or balun

## Average power of SSB telephony

Some components used for SSB telephony need not be capable of handling the Peak Envelope Power (PEP) continuously, many components for instance respond to the average power (Pav) which is quite less. Essentially, components that are subject to voltage breakdown (usually as good as instantaneous) must withstand the PEP, those that heat relatively slowly must withstand Pav.

In estimating the power dissipated in components due to an SSB telephony waveform, a good estimate of the ratio of Average Power (Pav) to Peak Envelope Power (PEP) is very useful.

Long before hams had used SSB, the figure has been of interest to designers of FDM or carrier telephone systems to size amplifiers that must handle n channels of FDM multiplex without overload which would degrade S/N in other channels of the multiplex. The methods are applicable to SSB telephony, it uses the same modulation type and the overload challenges are the same.

(Holbrook and Dixon 1939) gave the graph above which characterises the ratio of instantaneous peak to RMS voltage of voice telephony for different numbers of channels in a multiplex and different expectation of overload or clipping. They recommend a very low probability of clipping at 0.1% to avoid significant intermodulation noise in adjacent channels. Continue reading Average power of SSB telephony

## High end VSWR compensation in a ferrite cored RF transformer

The article Estimating the Insertion VSWR in a ferrite cored RF transformer discussed the importance of sufficient magnetising impedance to InsertionVSWR at low frequencies.

Above is a low frequency equivalent circuit of a transformer. Although most accurate at low frequencies, it is still useful for RF transformers but realise that it does not include the effects of distributed capacitance which have greater effect with increasing frequency.

The elements r1,x1 and r2,x2 model winding resistance and flux leakage as an equivalent impedance. Whilst for low loss cores at power frequencies, flux leakage is thought of as an equivalent inductance, purely reactive and proportional to frequency, the case of lossy ferrite cores at RF is more complicated. Winding resistance with well developed skin effect increases proportional to the square of frequency, but with lossy ferrite cores will often be dwarfed by the loss element of leakage impedance. Continue reading High end VSWR compensation in a ferrite cored RF transformer