About control of the dielectric constant of microwave substrates for boards. My experience

Before the introduction

I was prompted to write this article by one comment under my previous article, a man asked how I can be sure that the factory will make boards from the right material for me.

The second factor was that I was revising my old working photos and found one from the Keysight Technologies office (measurement equipment manufacturers)

The article describes my experience; I mentioned that there are many methods for measuring the parameters of materials, there are also many varieties of test coupons.

Introduction

I am a developer of microwave devices. If you open a physics textbook, the reader will learn that there are several types of transmission lines where an electromagnetic wave can propagate. Although waveguide technology is still indispensable in the mm range, for applications from, say, 1 to 30 GHz, printed lines are mainly used. In other words, microwave devices are made on the basis of printed circuit boards. For microwave printed circuit boards, special substrates are required (I wrote about the choice of a substrate earlier).

Unlike digital, analog circuitry uses many distributed elements – short sections of microstrip equivalent to a parallel capacitance, long spirals and short sections equivalent to inductance, etc. Almost all analog circuitry is built on quarter-wave sections, with the help of them decoupling for power supply can be realized, this is the main element of a transformer and, for example, a Wilkinson divider.

Fig. 1 Wilkinson divisor (picture from the Internet)
Fig. 1 Wilkinson divisor (picture from the Internet)
Fig. 2 Two-stage Wilkinson divider (picture from my Instagram)
Fig. 2 Two-stage Wilkinson divider (picture from my Instagram)

The wavelength in the material is inversely proportional to the root of the dielectric. permeability, therefore, with a deviation of die. permeability from the value according to the passport, which was used in the calculations, all characteristics “leave” in frequency.

For example, a Wilkinson divider at an operating frequency must have a minimum SWR and a minimum modulus. transfers between outputs. When changing the epsilon of the substrate, the quarters will be valid for a different frequency, the minimum SWR will be at a different frequency.

Experience in measuring the dielectric constant of a material

I wrote an article about my experience of ordering microwave boards in Russia. After all, I have not yet had experience of ordering boards in other countries. I know that many non-microwave developers order boards in China (this is evidenced by the many answers to my question to subscribers “where do you order boards?” By the way, I summarized all the answers in the table published in the mentioned article).

Once upon a time I had an interesting experience related to microwave boards from China. The fact is that when we (the department of microwave developers) received a batch of devices and began to measure their characteristics, we noticed oddities. The devices were complex, consisted of several microwave units, which is why it was difficult to immediately understand what was going on. The boss suggested that the epsilon of the material is slightly different than it should be. And we began to check this assumption. Since we only had our devices on hand, no scraps of material or whole sheets were sent to us, of course, we were limited in verification methods.

Methods for measuring parameters of materials can be divided into several groups.

Figure 3 Slides from a Keysight presentation
Figure 3 Slides from a Keysight presentation

Some of them are only suitable for liquids (coaxial probe), some only for relatively large samples (measurement with two antennas). We only had access to the measurement method in the transmission line, or rather, in the waveguide transmission line.

Preparation. We blew (not ourselves) all the foil from one of the boards. Cut a rectangle (even several) exactly the size of the waveguide. In addition, we prepared a couple more samples from a known material for verification.

Measurements. Keysight was kind enough to help us with these measurements. We used the PNA-X with the installed software for measuring the parameters of materials and such a set.

Figure 4 Keysight Waveguide Materials Measurement Kit (my photo)
Figure 4 Keysight Waveguide Materials Measurement Kit (my photo)

The method consists in the fact that a sample of known length and thickness, but with an unknown dielectric, is included in the transmission line. permeability. The vector network analyzer measures the coefficient. transmission at different frequencies and plots the dependence of epsilon on frequency.

Now in more detail. The set includes 2 coaxial-waveguide transitions (KVP), the section of the waveguide where the sample to be measured and the waveguide calibration set are inserted: matched load, XX and short-circuit. There are also special clamps that tighten the waveguide flanges.

Fig. 5 The process of measuring the parameters of materials.  Waveguide transmission line method (my photo)
Fig. 5 The process of measuring the parameters of materials. Waveguide transmission line method (my photo)

The photo above shows the coordinated load, in the foreground there are two KVPs, between them a segment of the transmission line should be placed. First, without anything, as in Figure 5, then you need to insert your sample there. Then the program will calculate the epsilon value by itself based on the comparison of the measured transmission coefficients. It is very important that the sample was cut exactly to the size of the waveguide (for example, we had a problem in small technological radii at the corners). Obviously, if there are gaps, the effective epsilon material + air will be shown.

Results. We then found out that the difference between the dielectric constant and the passport value was about 2%.

What can be done to prevent such troubles? Indeed, if on a simple diagram of one element, you can quite easily and quickly identify deviations, then on a complex device of several nodes it is much more difficult. Answer: test coupons (test coupons, most often resonators)

Test coupons

The simplest test coupon is an ordinary resonator in the form open stub.

Fig. 6 Resonator length l1, width W1
Fig. 6 Resonator length l1, width W1

At a frequency when the length l1 is equal to a quarter of the wavelength in the material, XX at the end of the resonator forms a short circuit at the junction point, thus on the frequency dependence of the modulus coefficient. transfer 21 will fail. My example with measurements:

Rice.  7 Resonator and its frequency response (pictures from my instagram)
Rice. 7 Resonator and its frequency response (pictures from my instagram)

One of the most common types of test coupons is a ring-shaped resonator, such an element has a higher Q-factor.

Fig. 8 A ring-shaped resonator and its equivalent circuit (picture from the Internet)
Fig. 8 A ring-shaped resonator and its equivalent circuit (picture from the Internet)

Ring resonators are sometimes supplemented with different elements to improve matching. For example:

Fig. 9 Ring resonator with trimmers
Fig. 9 Ring resonator with trimmers

Implementation. The first and easiest way is to add a board with a “test coupon” resonator when animating a workpiece with boards. Often there is no way to make a separate board, so you can place the resonator somewhere in a corner and make seats for vertical connectors.

Examples of vertical connectors

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