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April 25, 2021:
Revised: v1.0
Make Small Nano Henry RF Inductors Accurately
If you design and build your own VHF and UHF circuits then it's almost certain you will need to make small nano Henry (nH) inductors. The problem is to make these reasonably accurately. Here is my approach to making these little inductors.
Introduction
I’ve been designing and testing a number of VHF power amplifiers recently. Initially, I built a 10W VHF Class C RF power amplifier for single frequency operation using what I thought to be a well-proven design. It proved to be unstable and very difficult to align. That led to an extensive set of designs and tests using different semiconductors, output power levels and matching methods to identify a more reliable and stable power amplifier design.As part of this process, I needed to make lots of low value inductors ranging in value from 5nH to 100nH. The obvious question: How could I make such low value inductors accurately? How could I be confident those inductors had the correct inductance?
Internet Sources
Looking
on the web, there are a number of web pages that claim to be able to
calculate the length of wire and/or number of turns necessary for
inductors in this nH range. I began by making a few of these inductors.
However, when I fitted them into my power amplifier designs, this
quickly led to considerable head-scratching. The results were far from
those expected.This presented a challenge. I clearly had to verify the value of these small inductors. But how could I do this reasonably accurately with such small inductances?
Methods to Measure Small Inductors
I
have an LC Meter on my bench (Figure 1). It's actually one I designed
and built some years ago, loosely based on the very popular
LM311-based designs described everywhere. Actually, my version uses a
74HC04-based oscillator, an ATtiny85 processor, and an I2C LCD to
minimise the size of the meter and the current drain. I like my
batteries to last a long time! I can measure inductors down to the 5 - 50nH limits with this meter. It'salso reasonably stable, unlike many I have tried. Regardless, I was very doubtful as to its accuracy down at that low value nH range.
Figure 1 : My homemade LC meter
Looking around my workshop bench, I also had a reasonably accurate gate dip oscillator (GDO) which allows the resonant frequency of parallal LC circuits to be measured up to 250MHz, and an inexpensive Nano-VNA (50kHz to 900MHz).
Figure 2: My commercially made gate dip meter covers from 700kHz up to 250MHz with impressive accuracy for such an ancient, oops, I mean "legacy" instrument
Figure 3 : The Nano-VNA covers up to 900MHz and can provide moderately accurate impedance measurements
As the saying goes, a man with two watches is never certain of the exact time. If I included my LC meter, I potentially had three ways to measure these small nH inductors, each with its own advantages and disadvantages. With care, arguably the most accurate is the Nano-VNA. With similar care, the GDO is also sufficiently accurate to verify the Nano-VNA results. In turn, these would allow me to determine the accuracy of my LC meter.
Test Inductors
I
began by making a further series of inductors across a range of
different sizes. These were made from 24SWG, 28SWG and 34SWG enameled
copper wire, some bent into hairpin shapes, others into small coils, as
well as several larger coils of three to five turns, some using bare
copper wire, and even one made with plastic coated solid copper wire.
These were each measured using the GDO and the VNA. 
| 100mm | 25mm | 25mm | 22mm | 42mm | 34mm | 70mm |
| 80 - 110nH | 14nH | 15nH | 12nH | 30nH | 20nH | 55nH |
The GDO measured the resonance of each inductor when connected in parallel with a suitably sized capacitor, typically 15pF, 33pF or 47pF depending on the inductor size. The capacitors were measured on my LC meter. I was confident that the measurements were within 5% based on past results confirmed by measuring small value silver mica 1% tolerance capacitors.
I also used my Nano-VNA to measure the inductance of each inductor directly by mounted each one onto a male SMA connector and measuring the inductance across the 50 – 500MHz range.
Test Results
Here’s what I discovered:- Most
web-based inductance calculators are very inaccurate in this inductance
range despite claims to the contrary (That’s putting it politely).
- Small
inductors may be simply straight pieces of wire or the same wire length
bent into a hairpin (U-shaped) half-loop or twisted into small coils of
one of two turns. For inductors in the (say) 5 – 60nH range, the
resulting inductance hardly varies as the inductor shape is changed
from a straight wire, then into a hairpin loop, and finally the same
length twisted into a small one or two turn coil.
- Larger inductors made with, say, 4 to 6 turns, typically measured somewhere in the 50 – 100nH range. The inductance of the multi-turn coil was greater than the inductance of the same length of wire when “straight” or bent into a simple "hairpin" shape. The inductance typically increased by about 10% as the hairpin was wound into a wide-spread multi-turn coil (where each turn was spaced from its neighbor by say 5-10mm) and by up to about 20% if the wire was formed into a tight closely wound coil.
Predicting Inductance
To
simplify the presentation of these results and their future use in
VHF/UHF designs, I plotted the measured values on this graph. Only a
selection of the tested inductors are plotted on this graph.
Figure 2 : nH Inductor Wire Length
I’m summarizing my results here (so I can find them more easily when I need them!) It’s also possible this information may be useful for others, too. Just be aware - Your results may differ from mine.
My VHF power amplifier tests have definitely improved now I can install inductors of the correct value into each trial design!
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