NanoVNA – interpolation – part 5

NanoVNA – interpolation – part 4 and prior articles discussed the possibility of significant error when calibration data is interpolated.

This article illustrates the effects with some very simple examples.

Test scenario

The test scenario is a NanoVNA-H4 with 5m length of RG58A/U to the reference plane. It has been OSL calibrated at the reference plane using a 1-101MHz 101 point sweep.

Result without interpolation of the calibration dataset

Above is a zoomed in view of 1-5MHz of a 1-101MHz 101 point sweep, there are measurements at every whole MHz value from 1 to 101. There are only 5 measurement points on this graph. Continue reading NanoVNA – interpolation – part 5

NanoVNA – interpolation – part 4

NanoVNA – interpolation – part 3 discussed selection of a sweep step size to provide sufficient data points for reasonably accurate interpolation.

When / where is interpolation used?

The VNA correction process uses measurements of some known conditions to create a calibration dataset, a table if you like of the sweep frequencies and calibration data. Commonly the calibration dataset is a table of the correction factors calculated from measurements of the knowns for each frequency of the calibration sweep. The correction factors are usually calculated for each frequency independently of adjacent frequencies.

When used to sweep a different range, interpolation can be used to interpolate those correction factors to the new measurement frequencies.

A common data flow is that shown above, where the correction terms are calculated for each of the frequencies in the calibration sweeps, and then those terms are interpolated to the frequencies actually used for a DUT measurement sweep. Continue reading NanoVNA – interpolation – part 4

NanoVNA-APP v1.1.209-OD13 released

NanoVNA – interpolation – part 3 discussed interpolation and introduced cubic spline interpolation.

NanoVNA-APP v1.1.209-OD12 and prior used one of the special monotone types of cubic spline interpolation.

When used in VNA correction, the control points are often complex numbers with real and imaginary in broadly sinusoidal form and approximately 90° out of phase… so behavior on this scenario is important.

Above is a comparison of two types of interpolation on a pure sine wave. The green curve is the underlying sine curve, the orange dots are the samples or control points, the red curve is a linear interpolation, the blue dots are an example monotone cubic spline interpolation (monotone-cubic-spline.js). Continue reading NanoVNA-APP v1.1.209-OD13 released

NanoVNA – interpolation – part 3

This article continues on from NanoVNA – interpolation – part 1 and NanoVNA – interpolation – part 2 which illustrated jagged scans at up to 900Mhz where the reference plane was displaced by 5m of RG58A/U.

A quite practical example where care must be taken is the following one at HF. Let’s say you wanted to measure the feed point impedance of some HF antenna, and the online gurus explained that one way to do that was to calibrate the NanoVNA and normal antenna coax feedline as a fixture, setting the reference plane to the feed point end of the coax.

A Simsmith model for illustration

A Simsmith model was constructed of a 30m (~100′) length of RG213 with a short circuit termination, and the real and imaginary parts of s11 as would be seen by the NanoVNA were plotted.

Let’s say you wanted to sweep from 1.5-33MHz (to include a little each side of the 160-10m bands… partly for reasons to be explained later.)

30m of RG213 @ 33MHz, step size 0.3MHz

Lets focus on the high frequency end where the jagged response is worse.

Again we see the periodic variation of s11 real and imaginary components as shown in the earlier articles. In the plot above, Simsmith as done a linear interpolation of the sweep points, and at 0.3MHz per step, the curves a jaggy. The actual minimum of the blue curve is at 33.88MHz, and the value is about 5% higher than the linear interpolation… which will introduce measurement noise to any VNA sweeps with such a configuration. Sweeps such as this are inputs to the calibration process. Continue reading NanoVNA – interpolation – part 3

NanoVNA – interpolation – part 2

NanoVNA – interpolation – part 1 introduced the principle on which VNA measurements are made and corrected based on a set of error terms derived from measurement of some known loads at the reference plane.

The technique of interpolation as a convenient means of increasing the utility and flexibility of a calibration data set was also introduced, and example raw (uncorrected) sweeps of an OC at the end of about 5m of RG58A/U were given to illustrate the challenge in interpolation with insufficient samples or control points.

A more common data flow is that shown above, where the correction terms are calculated for each of the frequencies in the calibration sweeps, and then those terms are interpolated to the frequencies actually used for a DUT measurement sweep. Continue reading NanoVNA – interpolation – part 2

NanoVNA – interpolation – part 1

A simple two port VNA allows measurement of  S parameters s11 and s21 of a DUT. Port 1 contains a directional coupler to transmit a signal into the DUT, and to capture and measure the amplitude and phase of the reflected wave relative to the forward wave at Port 1 (s11). Port 2 simply measures the amplitude and phase of the signal at its input, the forward wave after it has passed through the DUT relative to the forward wave at Port 1 (s21).

This is typically done by stepping (sweeping) the source on Port 1 through a range of frequencies, specified for example by start and end frequency and the number of discrete steps.

There are several source of error in such a measurement, but by making a series of measurements of some known configurations (Short, Open and Load on Port 1, Isolation and Through to Port 2), those errors can be determined and corrected out of subsequent measurements. So, there is a calibration process to measure and save measurements on these known loads, and then a correction process to apply the calculated corrections to raw measurements.

Early VNAs invalidated the calibration data if sweep parameters were changed, and so corrections were applied to raw measurements at corrections measured and calculated at exactly the same frequency.

This was really inconvenient, especially where no facility was provided to permanently save and restore a set of calibrations.

Later VNAs included the facility to interpolate (but not extrapolate) the calibration / correction data to a new set of sweep parameters. This was really convenient, but introduced a new source of error, the interpolation error.

When all this is done under the covers, users with little understanding of what is going on under the covers can easily obtain invalid / worthless results.

Let’s focus on s11 measurement, though the same issues exist for s21 measurement.

Above is a plot of uncorrected or raw s11 sweeping a NanoVNA-H4 101 points from 1 to 900MHz with nothing on Port 1 (approximately an open circuit OC). Ideally s11 should be 1+j0, but the directional coupler circuitry and small distance to the connector means the amplitude and phase vary as shown in the plot. Continue reading NanoVNA – interpolation – part 1

Can a diode be used to rectify signals smaller than its ‘threshold’ voltage?

Several articles on this site have used diode half wave detectors down to very low signal levels, well below the commonly perceived ‘threshold’ of the diodes, and it has prompted comments to the effect that this cannot work.

Really simple PN junction diode model

An ideal diode is a device that conducts in one direction with zero voltage drop, and does not conduct in the other direction.

Practical diodes typically have an IV characteristic with a knee at some small forward bias from about 0.2V to 0.6V depending on the nature of the PN junction.

An often used simple model of a practical diode is an ideal diode with a series battery of voltage equal to the offset of that knee, the ‘threshold’ if you like.

This model may be quite adequate when the applied voltage is much larger than the knee voltage, eg if you were rectifying 24V AC.

Practical diodes

Shockley’s diode equation

William Shockley modelled the IV characteristic of a diode as \(I_D=I_S(e^{\frac{V_D q}{n k_B T }}-1)\) where ID is the diode current, IS is the reverse-bias saturation current (or scale current), VD is the voltage across the diode, kB is Boltzman’s constant, T is absolute temperature, q is an elementary charge, and n is the ideality factor, also known as the quality factor or emission coefficient.

\(\frac{k_B T }{q}\) is often known as VT.

Shockley’s equation with n=1 is often known as Shockley’s ideal PN diode.


Let’s look at the BAT46 Schottky diode, it has PIV=100V and is very suited to a lot of these higher voltage RF signal projects.

Above is the IV characteristic from a datasheet. They are often not very helpful at really low currents as used in some of these applications, but note the  great temperature sensitivity. Continue reading Can a diode be used to rectify signals smaller than its ‘threshold’ voltage?

R2009D oscilloscope input impedance

The Motorola 2009D incorporates a basic oscilloscope function, specified with bandwidth of 0.5MHz and input impedance of 1MΩ. The input impedance specification is naively incomplete, there will be some parallel equivalent capacitance that is very important to selecting a compatible probe.

Above is the schematic of a test circuit to find that input capacitance Cin. Continue reading R2009D oscilloscope input impedance