# OSHPark 4 Layer PCB Measurements

## Intro

OSHPark PCBs are convenient for various RF test boards at a low cost given the relatively low loss Isola FR408 material. Trying an idea is much more appealing when the cost is $50 for the board and parts versus$1000+ for a custom RF material stack up prototype. As you will see there is some variation in properties over the board. These are built with prepreg for outer layers where RF and microwave PCBs typically have cores for outer layers for consistent dielectric thickness. These have been used succesfully at Harmon Instruments to beyond 50 GHz. Loss is extremely high at those frequencies, so lines must be kept short. There is a bypassable frequency doubler in the VNA that measured this data on an OSHPark PCB, providing stimulus from 26.5 GHz to 50 GHz.

Thanks to OSHPark for providing this board and the previous revisions at no charge.

## The test board

The first revision used line widths calculated from the values on the OSHPark site. Impedances were consistenly high (56 ohms typical) over two orders of the board. This one uses the assumption of 0.19 mm thick prepreg with an Er of 3.3 (versus 0.17 mm and Er of 3.66) given in the OSHPark docs. See the previous blog post for the Er of just the material. The missing corner of this board was the sample used there. The prepreg in the cross section measures approximately 0.177 mm, but likely varies throughout the board. The total thickness varies about 25 µm over a board.

## Microstrip

##### Time Domain

0.42 mm wide lines are used for 50 ohm microstrip on this board. As can be seen in the plot above, the impedanace is, on average, a bit low. Perhaps, 0.41 mm would be a good design value. PCB #1 had the most variation and the impedance correlates with PCB thickness variation along the line. There is a short thick area around the high impedance peak. The other two show a thickness taper along the length. I repeated the measurement of PCB #1 after #2 and #3 and got data nearly indistinguishable from the original measurement.

Using the same 0.42 mm width, but adding solder mask, gives a lower impedance of around 47 ohms. A good design value to achieve 50 ohms might be 0.39 mm. Covering microstrip in solder mask does save some insertion loss, but the difference is minimal, so unmasked may still be preferred.

##### Effective Relative Permittivity (Er)

Effective Er is simply the square of the speed of light divided by the propagation velocity in the line.

The unmasked microstrip should have an effective Er of around 2.5 given the assumptions about Er and the line geometry. It measures much higher. I presume this is due to metal loss and surface texture, but am not certain of it. Comments are welcome. I measure ErEff=1.002 for 3.5 mm air lines at 20 GHz using the same differential phase calculation. EM simulation shows that a textured conductor has slower propagation than a smooth one and this is rather rough copper. The plot below shows time domain step responses of both 53 mm lines with the masked line reaching 50% at 309.4 ps and the unmasked at 296.4 ps. Those correspond to effective Er values of 3.07 and 2.81. The effect of the mask slowing propagation is clearly visible. The stimulus rise time (10-90%), (set by the window function) is about 14 ps, masked is 25 ps and unmasked is 36 ps.

## Stripline

The striplines on this board are 0.3 mm wide, on inner2, with copper on inner1 and the bottom as ground references. It's very close to 50 ohms. The vias need a bit more clearance (0.2 mm used on this board) as can be seen by the low impedance spikes in the time domain plot.

##### Time Domain

The 2.4/1.85 dip is the discontinuity resulting from the connection of a 2.4 mm and 1.85 mm connector. A similar discontinuity results from connecting a 2.92 to a 3.5 mm connector. The Harmon Instruments VNA supports removal of these discontinuities, but it was not enabled here. The via dips are the vias transitioning from microstrip to stripline.

##### Insertion Loss

The spikes at ~ 2 GHz intervals are artifacts of the LRL on PCB calibration (frequencies where the line phase difference is 180 degrees) and should be ignored. More lines could have been added to avoid these.

##### Effective Er

The Er of the core is about 4.0 and the prepreg 3.3. Electromagnetic simulation without metal loss gives an effective Er of 3.55 for this geometry. Like the microstrip case, these values are higher than expected. The values are higher at low frequencies primarily due to metal losses. Stripline is often stated to be free of dispersion, but that assumes lossless materials.

## Components

This one is simply a 49.9 ohm 0402 resistor in series with 1 mm of 50 ohm line on either side and was done as a check on the impedance calibration. The result is as expected.

I'd previously measured these two ferrite beads with no DC bias, but had questioned how much that would change the inductance. The effect is significant at low frequency and small at higher frequencies. It's interesting that the order of the traces reverses above the self resonant frequency as the decreasing shunt inductance reduces the effective capacitance. These ferrite beads are mostly capacitive above the parallel resonance. The VNA bias tees contribute only a negligible amount (0.002 dB insertion loss increase at 200 mA) to this data.

These parts are both capacitive at higher frequencies and the above performance could be improved by adding short high impedance sections to either side of the ferrite bead. About 120 pH on either side should give the BLM15GG471 20 dB return loss to 30 GHz.

# Measuring Material Properties in Waveguide

I saw Dielectric constant measurement for thin material at microwave frequencies and wanted to give it a try. This was done in WR-42 waveguide from 18 to 26.5 GHz. Samples were cut to 0.17 x 0.42 inches to fit the waveguide.

## Relative Permittivity (Er)

Material Thickness Er (measured) Er (ref)
Polypropylene (pp) 736 μm 2.14 2.26 at 9.4 GHz
Polycarbonate (pc) 583 μm 2.7 2.77 at 11 GHz
Rogers RO4350B 509 μm 3.59 3.48/3.66 at 10 GHz
OSHPark 4 layer prepreg 205 μm 3.3 3.26 - 4.01
OSHPark 4 layer core 531 μm 4.02 3.26 - 4.01
GE Silicone II (white) 1.875 mm 2.64 unspecified
##### OSHPark PCB

The OSHPark 4 layer PCBs are made from Isola FR408. As shown in this document, the thicker cores and prepregs have higher glass content and thus higher Er. The 47 mil thick core is not listed in the above PDF, but would presumably be the heaviest glass and have an Er of around 4.0. The prepreg used for the outer layers is a fine glass weave with high resin content, so the measured value of 3.3 seems reasonable. The prepreg sample is very thin and has some taper, so that value may be the least reliable of the group. The core and prepreg samples were obtained by mechanically delaminating a finished PCB.

##### RO4350

The RO4350B has a 10 GHz dielectric constant of 3.48 +- 0.05 using a clamped stripline method that tends to underestimate Er on hard materials like RO4350B. The recommended value for design is 3.66, so this measured value of 3.59 seems reasonable.

##### Silicone II

This is white caulk from a hardware store which I had purchased for my bathtub. The data on this one is questionable as it was hard to cut a precise block of this soft material. A silicone might be interesting as a directional coupler overlay.

## Loss Tangent

These values are less reliable and noisy as the dissipation loss of the samples is on the order of 0.015 dB. The polypropylene has such low loss that errors are causing it to appear to have a negative loss tangent. The waveguide shim used as a sample holder was bare brass which certainly didn't help repeatability. The spikes in the silicone and osh_core traces are likely due to resonance within the sample as the section of guide containing the sample can support higher order modes.

## Approximation not valid

The plot above shows the amount of error introduced by the assumption in the paper that the samples are thin. The data with _est uses the approximations for small values, $$\sin(kz_2\tau) \approx kz_2\tau$$. With the smaller guide and higher frequencies used here versus the original paper, the assumption is not valid with reasonable thickness samples.

The value of Er is solved for using SciPy optimize.minimize. It's a bit ugly as it doesn't directly handle complex numbers, but gets the job done.

## Future work

Try to do something similar in 7 mm coax.

## Code

The SParameter library (used for opening .s2p files, wgsection, S parameter concatenation) has not yet been released, so this is only useful for reference. The library is in C++ with SWIG wrappers and will be released as open source (GPLv3) when it is ready.

#!/usr/bin/env python3
import numpy as np
import matplotlib.pyplot as plt
import sys
sys.path.append("../../")
import SParameter as scpp
from scipy.constants import c, inch
import scipy.optimize

a = 0.42 * inch # wide waveguide dimension in meters

samples = [ # file name, thickness in meters
['pc.s2p', 583.0e-6],
['pp.s2p', 736.0e-6],
['ro4350b.s2p', 509e-6],
['osh_prepreg.s2p', 205e-6],
['osh_core.s2p', 531e-6],
['silicone.s2p', 1875e-6],
]

for sample in samples:
fn = sample[0]
t = sample[1] # thickness
sp = scpp.SParameter(fn)
sp.reducefreqrange(50e6, 18e9, 26.5e9)
# add an air filled section of guide the length of the sample
te = scpp.wgsection(sp, a, t)
sp = scpp.SParameter(te, sp)
s = np.array(sp.s)
s21 = 0.5 * (s[1::4] + s[2::4]) # average of s21, s12
f = np.array(sp.f)
e = np.zeros(len(f), dtype=complex)

for i in range(len(f)):
wavelength = c / f[i] # free space wavelength
kz = (np.pi/(wavelength*a)) * np.sqrt( 4.0*np.square(a)-np.square(wavelength))

def func(z):
c = s21[i] - 1.0 / (np.cos(z) + 0.5j*kz*t*(1+np.square(z/(kz*t))) * np.sin(z)/(z))
return c.real*c.real + c.imag*c.imag

b0 = [a.real, a.imag] # estimate, assumes Er = 1.0
res = scipy.optimize.minimize(lambda z: func(complex(z[0],z[1])), b0, tol=1e-6)
kz2 = complex(res.x[0], res.x[1])/t
e[i] = (np.square(kz2 * wavelength * a / np.pi) + np.square(wavelength))/(4*a*a)

if sys.argv[1] != 'loss':
plt.plot(f/1e9,np.real(e), label=fn)
plt.ylabel('Er')
else:
losstan = -np.imag(e)/np.real(e)
plt.plot(f/1e9,losstan, label=fn)
plt.ylabel('loss tangent')

plt.xlabel('Frequency (GHz)')
plt.legend(loc=4)
plt.grid(True)
plt.show()


# Unit Testing VNA Calibration Code

### The Problem

There are an alphabet soup of VNA calibration types (SOLT, TRL, LRL, TRM, SOLR, QSOLT, many more), some of which will be supported by the Harmon Instruments VNA and run by the end user. Testing all of the supported calibration types through the normal user interface and measuring verification components for each could easily take an entire day. Using physical calibration standards, uncertainties would be limited to those of the standards. An additional concern with testing on hardware is the wear and tear on the fragile and expensive calibration standards.

### Breaking it Down

The data path from ADC values to corrected S-parameters for display is split into layers with independent test coverage. The lowest level, implemented in an FPGA, taking signals from the ADCs has test coverage using the excellent CocoTB package. The next layer, written in C++, takes integer vector voltage data from the FPGA and produces raw S-parameters. These first two layers are relatively simple mathematical operations. The final layer, correcting the raw S-parameters, is where the complexity lies and is what will be discussed here.

### Modeling the VNA and Calibration Standards

For simplicity, we will focus on a 2 port VNA calibrations using an 8 term error model (TRL, SOLR, similar). This model contains a fictitious 2 port "error adapter" to either side of the device under test (DUT). These represent internal leakages, losses, gain imbalances, etc as well as the test port cables. The raw S-parameters are simply those of the DUT in cascade with the two error adapters. In a calibration, sufficient standards are measured to solve for the error adapters.

Knowing the contents of the error adaptors, it is possible to run the calibration backwards and calculate the raw S-parameters from the true S-parameters of the devices being measured. Realistic models of the calibration standards are used with airlines, opens and shorts having loss. Simulated raw data is genereated for the required set of standards as well as a few challenging DUTs and the data is sent throught the calibration acquisition and correction software. The corrected data is compared with the originals and verified to be within reasonable rounding error. The tests on the calibration algorithms complete in less than 1 second and run every time the software is built causing the build to fail if any test does.

For the purposes of testing the calibration software, the VNA is presumed to be linear and time invariant. In the future, for uncertainty analysis, it may be desirable to add drift and nonlinearity based on characterization of real hardware.

### Offline Processing of Acquired Data

By saving raw data for many types of calibration and verification standards, it is possible to generate corrected S-parameters using any calibration type using those standards. QSOLT had not yet been coded when this data set was aquired, but it is possible to generate QSOLT corrected data as all of the required standards are present in the data dumps. This is mostly useful to see how the algorithms compare with imperfect standards.

The above plot shows significant differences between calibrations assuming the load standards are ideal (QSOLT, TRM), TRL which uses airlines rather than loads and a data based QSOLT calibration which uses more accurate models of the short, open and load. These differences are not due to software, but the physical standards and their definitions.

### Implementation

The S-parameter handling code (C++) on the Harmon Instruments VNA has a SWIG generated Python wrapper and the Python unit testing framework is used to run the tests. Google Test would have been another option. Python works well here due to libraries like NumPy, SciPy and Matplotlib providing mathematical functions and plotting. For instance, to test a C++ implementation of the Kaiser window, I added a test to compare it with one generated by SciPy.