## Noise figure of active loop amplifiers – the Ikin dynamic impedance method

Noise figure of active loop amplifiers – some thoughts discussed measurement of internal noise with particular application of active broadband loop antennas.

(Ikin 2016) proposes a different method of measuring noise figure NF.

Therefore, the LNA noise figure can be derived by measuring the noise with the LNA input terminated with a resistor equal to its input impedance. Then with the measurement repeated with the resistor removed, so that the LNA input is terminated by its own Dynamic Impedance. The difference in the noise ref. the above measurements will give a figure in dB which is equal to the noise reduction of the LNA verses thermal noise at 290K. Converting the dB difference into an attenuation power ratio then multiplying this by 290K gives the LNA Noise Temperature. Then using the Noise Temperature to dB conversion table yields the LNA Noise Figure. See Table 1.

The explanation is not very clear to me, and there is no mathematical proof of the technique offered… so a bit unsatisfying… but it is oft cited in ham online discussions.

I have taken the liberty to extend Ikin’s Table 1 to include some more values of column 1 for comparison with a more conventional Y factor test of a receiver’s noise figure.

Above is the extended table. The formulas in all cells of a column are the same, the highlighted row is for later reference. Continue reading Noise figure of active loop amplifiers – the Ikin dynamic impedance method

## Review of noise

Let’s review of the concepts of noise figure, equivalent noise temperature and measurement.

Firstly let’s consider the nature of noise. The noise we are discussing is dominated by thermal noise, the noise due to random thermal agitation of charge carriers in conductors. Johnson noise (as it is known) has a uniform spectral power density, ie a uniform power/bandwidth. The maximum thermal noise power density available from a resistor at temperature T is given by $$NPD=k_B T$$ where Boltzmann’s constant kB=1.38064852e-23 (and of course the load must be matched to obtain that maximum noise power density). Temperature is absolute temperature, it is measured in Kelvins and 0°C≅273K.

## Noise Figure

Noise Figure NF by definition is the reduction in S/N ratio (in dB) across a system component. So, we can write $$NF=10 log \frac{S_{in}}{N_{in}}- 10 log \frac{S_{out}}{N_{out}}$$.

### Equivalent noise temperature

One of the many methods of characterising the internal noise contribution of an amplifier is to treat it as noiseless and derive an equivalent temperature of a matched input resistor that delivers equivalent noise, this temperature is known as the equivalent noise temperature Te of the amplifier.

So for example, if we were to place a 50Ω resistor on the input of a nominally 50Ω input amplifier, and raised its temperature from 0K to the point T where the noise output power of the amplifier doubled, would could infer that the internal noise of the amplifier could be represented by an input resistor at temperature T. Fine in concept, but not very practical.

### Y factor method

Applying a little maths, we do have a practical measurement method which is known as the Y factor method. It involves measuring the ratio of noise power output (Y) for two different source resistor temperatures, Tc and Th. We can say that $$NF=10 log \frac{(\frac{T_h}{290}-1)-Y(\frac{T_c}{290}-1)}{Y-1}$$.

AN 57-1 contains a detailed mathematical explanation / proof of the Y factor method.

We can buy a noise source off the shelf, they come in a range of hot and cold temperatures. For example, one with specified Excess Noise Ratio (a common method of specifying them) has Th=9461K and Tc=290K. If we measured a DUT and observed that Y=3 (4.77dB) we could calculate that NF=12dB. Continue reading Noise figure of active loop amplifiers – some thoughts

## Rigexpert Antscope2 – v1.1.1

A new version of Antscope2 has been released.

Online posters are excited that it supports some versions of nanoVNA, and one thread attempts to answer the questions:

The SWR image shows that the SWR minimum is at the center phase angle as you would expect. My question is:

1. what are the other points that look like resonance,

2. and should I trim my antenna based on phase?

3. If so which one?

They are interesting questions which hint the ham obsession with resonance as an optimisation tartget.

Properly interpreting VNA or analyser measurements starts with truly understanding the statistic being interpreted.

In this case, the statistics being discussed are Phase and VSWR, and their relationship.

What is the Phase being discussed?

Above is an Antscope2 phase plot for an archived antenna measurement. The measurements are of a 146MHz quarter wave mobile antenna looking into about 4m of RG58C/U cable. We will come back to this. Continue reading Rigexpert Antscope2 – v1.1.1

## Rigexpert AA-600 N connector dimensions

A recent post by David Knight described dimensional issues with the N connector on his AA-600 and problems with the seller in having it resolved.

Warned of a potential quality issue, I measured my own AA-600.

Above, the test of the inner pin forward surface distance from the reference plane on the N jack on the AA-600. The acceptable range on this gauge for the female connector is the red area, and it is comfortably within the red range.

Above is a table of critical dimensions for ‘ordinary’ (ie not precision) N type connectors from Amphenol.

This dimension is important, as if the centre pin protrudes too much, it may damage the mating connector.

Pleased to say mine is ok, FP at 0.192″.

I used a purpose made gauge to check this, but it can be done with care with a digital caliper (or dial caliper or vernier caliper), that is what I did for decades before acquiring the dial gauge above.

## VSWR ripple

Having seen some recent discussion where the online experts opined that an example given of a VSWR plot that contained a fairly consistent ripple was quite normal, this article suggests there is an obvious possible explanation and that to treat it as quite normal may be to ignore the information presented.

Above is a partial simulation of a scenario using Rigexpert’s Antscope. It starts with an actual measurement of a Diamond X-50N around 146MHz with the actual feed line de-embedded. Then a 100m lossless feed line of VF=0.66 is simulated to produce the plot that contains a ripple apparently superimposed on an expected V shaped VSWR curve.

This is the type of ripple that the expert’s opine is quite normal. Continue reading VSWR ripple

## Reinforcement of nanoVNA-H connectors – performance discussion

At Strength of reinforcement of nanoVNA-H connectors I showed a method I used to reinforce the SMA connectors to reduce the flexing of the PCB when the SMA connectors were torqued to specification for reliable measurement.

This has been commented on by online experts stating that Hugen, the designer of this board, posted notes about his efforts to keep the grounds for tx and rx port circuits isolated to some extent.

Opinion by some is that the modification I performed above which electrically bonds the two connectors through a brass bar of about 60mm length is likely to significantly degrade performance. Continue reading Reinforcement of nanoVNA-H connectors – performance discussion

## A thinking exercise on Jacobi Maximum Power Transfer #4

The article A thinking exercise on Jacobi Maximum Power Transfer #3 discussed Kurokawa’s power reflection coefficient as in indicator of mismatch at a system node.

Above is a demonstration circuit in Simsmith, a linear source with Thevenin equivalent impedance of 50-j5Ω. The equivalent voltage is specified by useZo, which like much of Simsmith is counter intuitive (as you are not actually directly specifying generator impedance):

Vthev and Zthev are chosen so that ‘useZo’ will deliver 1 watt to a circuit impedance that equals the G.Zo. Zthev will be Zo*.

## The transmitter matching problem

In the article The system wide conjugate match stuff crashes out again I worked through an example proffered in an online discussion to show that Walter Maxwell’s teachings on system wide simultaneous conjugate match do not tend to occur in practical systems.

## Why are hams so obsessed with conjugate matching?

The answer is on the face of it quite simple. Continue reading The transmitter matching problem

## Strength of reinforcement of nanoVNA-H connectors

The nanoVNA-H connectors are end launch PCB connectors and they have a decidedly spongy feel as 1Nm torque is approached. This was due to flexing of the PCB and was likely to lead to track cracks in the longer term.

Specs for SMA connectors range from minimum of 0.2Nm torque to maximum of 1.7Nm, but 0.6Nm and 1.0Nm are common commercial practice.

Some nanoVNA sellers state:

As the SMA ports are made of cast copper, please not connect hard 50-7 / RG213 and other cables directly to the SMA ports through M-to-SMA connector to avoid damaging the SMA ports. You can use the included SMA cable to connect to the SMA port as shown in the picture below, and then use M to SMA connector.

Clearly Chinese Cheats, they will say anything to make a sale and anything to avoid commitment to quality. These connectors are very unlikely to be copper, but are likely to be a copper alloy: brass. What they also avoid in the above statement is claim for PCB damage due to flexure of the SMA connectors torqued to accepted industry torque for reliable connections and measurement.

Above is a pic of a modification to reinforce the connectors. This article sets out the analysis of just the solder joint within the cross section of the brass pieces.

A side effect is that this modification bonds the ground planes for the input and output parts of the nanoVNA via the brass bar where they have been kept isolated to some extent.

I should note that there has been much discussion online as to whether the noise floor of the nanoVNA is degraded by the shields fitted to the board, and various modifications to the shields. Some of this discussion proposes that the issue is mostly around the mixers and noise loops, and I note that in -H designs prior to v3.3, the mixer power supply was not adequately decoupled. It is possible that electrical connection of the SMA connectors in this way degrades noise performance at some frequencies. No significant change was observed in the noise floor of s11 or s21 channels from 1 to 300MHz (I don’t regard instrument performance to be good above 300MHz). I have not seen credible evidence of degradation of the nanoVNA-H v3.3 build.

If indeed bonding the two SMA connectors close to the instrument increases the noise floor or has other performance impacts as suggested, it questions whether the currents on the exterior of the coax influence measurement (which it should not) and it questions whether two port measurement fixtures or adapters should  be attached close to the nanovna.

At first, the strength of the butt soldered joint might seem a simple case of beam analysis where the beam is of cast solder of the same cross section l x w as the soldered joint. Continue reading Strength of reinforcement of nanoVNA-H connectors

## A thinking exercise on Jacobi Maximum Power Transfer #3

At A thinking exercise on Jacobi Maximum Power Transfer #2 I posed the question of a metric for the mismatch at the L2L1 junction in the following network where the calculated values L2L1_lZ is the load impedance at the L2L1 junction (looking left as Simsmith is unconventional), and L2L1_sZ is the source impedance at the L2L1 junction (looking right). The left three components are the fixed antenna representation.

Common practice is to speak of a “source VSWR” to mean the VSWR calculated or measured looking towards the source, and very commonly this is taken wrt 50+j0Ω which may be neither the source or load impedance but an arbitrary reference. Continue reading A thinking exercise on Jacobi Maximum Power Transfer #3