Hairpin filter design


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Electronics - 31-10-2018

What is a hairpin filter?

Electronic filters are circuits which remove unwanted frequency components from the signal to enhance wanted ones. They are notably useful in the radio UHF range, to remove undesired transmissions and therefore improve the relative receiver's sensitivity.

An SDR (software design radio) such as the RTL-SDR with good filtering and an adequate antenna (and possibly external amplification), can pick up lower amplitude signal (such as satellite transmissions).

Filters are usually made of discrete components (capacitors, inductors, etc.) in certain arrangements to form low-pass, high-pass, band-pass or band-cut. As frequency grows, this becomes increasingly unreliable. Microstrip filters are a higher-frequency alternative that uses the physical shapes and positions of transmission lines to affect their attenuation of certain frequency ranges.

There are many component forms used to construct distributed element filters, but all have the common property of causing a discontinuity on the transmission line. These discontinuities present a reactive impedance to a wavefront traveling down the line, and these reactances can be chosen by design to serve as approximations for lumped inductors, capacitors or resonators, as required by the filter.

My microstrip filter One of my 1090MHz hairpin microstrip filters, made using this generator.

The hairpin topology uses parallel-coupled lines and behaves like a band-pass filter used to isolate the bandwidth's frequencies from parasitic signals. It takes up relatively low board space and it quite easy to build compared to other band-pass microstrip topologies such as the interdigital filter.

There are a lot of papers describing the mathematical models of microstrip filters. However, it is quite hard to extract a recipe and it will often result in poor performance. Hence, I created this Javascript tool to generate them using a sensible experimental model.

The microstrip hairpin filter generator

Enter your desired center frequency in the following form to generate your SVG to be printed at 100% scale.

This hairpin configuration must be printed on one side of a standard double sided 1.6mm thick PCB. The back side must stay copper coated and be connect to the ground. The horizontal line at the bottom of the page is 150mm, to check scaling after printing.

The generated topologies are designed to be used with standard female 50Ω SMA board-edge connectors. Solder the connector center signal pins to the hairpin feeder tracks and the ground pins to the bottom side.


Technical details

Physics/Formulae

The following figure shows the structure of the hairpin filter:

A 3 hairpin filter physical structure.

The dimensions I used are given is the following table.

Dimension 3 Hairpin
D1 0.25 mm (10 mil)
D2 2 mm (80 mil)
D3 2 mm (80 mil)
Width 2.54 mm (100 mil)

The length is computed on a formula I determined with experimental data using a quadratic regression curve fitting:

Length [mil] = 4554 - 4.23 \times f_{center} + 1.17  \times f_{center} ^{2} \times 10^ {-3}

This gives very good results up to about 1.5GHz - more about this below.

PCB fabrication

To make my test hairpin filters, I used my quick prototyping method (click here to go to the article).

Photo of the masked hairpin PCB The masked copper board, ready for etching with ferric chloride.

This method is not well suited to achieve the precision that is required for the UHF range. Better PCB quality will result in less losses, improved consistency and a sharper frequency response.

Tests

Using my homemade scalar network analyzer (more on this in a future article), I measured the response of a 1120MHz center frequency hairpin filter made with this generator. This is the result:

Frequency response of a 1120MHz hairpin filter

We can see on this graph that the lower cutoff is very sharp. The upper cut is a lot rounder. This is unfortunately due to the nature of the filter. Four hairpins filters get a sharper cutoff at the cost of more losses.

It also shows that the bandwidth's attenuation is quite high. With more precise PCB manufacturing, it should be -5 to -8dB. However, this is easily solved with a simple 10dB LNA (low noise amplifier) added before or after the filter. Alternatively, the internal LNA in RTL-SDR's tuners should be able to deal with this, with a low NF (noise floor).

Fine tuning

The response of the filter depend of the diaelectric constant of the PCB material. To get a good estimation of your PCB's characteristic, the best way is to empirically determine your PCB coefficients by:

  • Manufacturing a filter using my calculator at your desired center frequency -20% (length=l1) and measure its true center frequency (f1),
  • Manufacturing a second filter at your desired center frequency +20% (length=l2) and measure its true center frequency (f2),
  • Compute your PCB material characteristic with the simple linear regression formula:

Length(f)={\frac{l_2-l_1}{f_2-f_1}}f+{\frac{f_2l_1-f_1l_2}{f_2-f_1}}

Because the relation between length and center frequency is nearly linear, this gives very good results.

Using good quality PCB, my generator alone should get your center frequency well within the bandwidth.

Limits

The lower frequency limit to hairpin filters is simply due to their physical size: below 900MHz, it gets quite big and therefore expensive. Of course, with some tuning, it is possible to get much lower than this.

The upper frequency limit is a bit more tricky: as frequency grows, the PCB material losses also grow. Above around 1.5GHz, with conventional FR4, they usually get out of control. Additionally, the filter's the cutoff shape gets gradually rounder and rounder. These two effects combined defeat the purpose of a filter.

However, distributed elements filters like the microstrip hairpin are commonly used in test equipment and satellite television reception for frequencies well above 5GHz. This is made possible thank to well controlled PCB material, high quality manufacturing processes and a lot of engineering!

The PCB inside a 20GHz Agilent N9344C spectrum analyzer

The PCB inside a 20GHz Agilent N9344C spectrum analyzer, photo by Binarysequence on Wikipedia

Sources

Author: Charles Grassin


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