Testing a Handmade Conical Inductor Against an Ordinary Solenoid Coil
イチケン / ICHIKEN
Conical inductors are wound in a cone shape, and few people in electronic circuit design have seen or used one. The presenter says a conical inductor works the same way as any other inductor. The video asks what the cone shape adds. The answer given is that it widens the frequency range over which the part keeps acting as an inductor. The presenter explains why this matters using a high-frequency amplifier, then builds a conical inductor by hand and measures it against a conventional coil. At least within the frequency range they could measure, the result did not come out the way they hoped.
What a Conical Inductor Is
Most inductors are wound as solenoids, as concentrated windings, or around a core such as ferrite. A conical inductor's winding gets steadily wider from one end to the other. The presenter says this shape is meant to broaden the band over which the component behaves as an inductor. To show why that matters, they walk through a circuit where such a part might be used.
Why an RF Amplifier Needs an Inductor in Its Bias Path
The example is a high-frequency amplifier. An RF signal comes in from the left, passes through a transistor, and leaves as RF output. A signal source and a transistor are not enough to make this work. The transistor also needs a DC bias circuit and a power supply. That supply line normally has capacitors hanging off it to smooth the supply and send power-supply noise to ground.
The presenter asks what happens if the bias supply is connected straight to the transistor. For DC, it works: the transistor gets its bias. The AC signal is a different story. The RF input comes in through a capacitor and meets the transistor, but it also meets the power-supply section. A capacitor's impedance falls as frequency rises, so the high-frequency signal flows into the bypass capacitor on the supply line instead of into the transistor. The presenter concludes that the transistor then can't amplify the signal, or, at best, would have low gain.
They then look at the same circuit from the supply side. Any supply noise the capacitor fails to remove could reach the transistor. There it might be amplified, and it could leak onto the RF signal path. With a direct supply connection, the presenter says, the transistor might be biased, but amplifying a signal looks difficult.
Putting the Inductor Back In
Next the presenter restores an inductor between the supply and the transistor. The inductor passes DC, so the bias still works. For AC signals the inductor has high impedance, so the RF signal from the source does not go into the inductor. It goes to the transistor, and the circuit can amplify properly.
The output side works the same way. An inductor there keeps the amplified RF signal from flowing back into the supply, so it goes to the RF output instead. The presenter notes that an inductor combined with a DC-blocking capacitor like this is called a bias tee.
Self-Resonance and Why It Limits Bandwidth
Any inductor will not do here. The right choice depends on the amplifier's operating frequency. For a wideband amplifier, the inductor must behave as an inductor across the whole band. The presenter first says its self-resonant frequency should be as high as possible. Then they refine the point: the real goal is to design the inductor so that no self-resonant frequency falls inside the band the circuit must handle.
Self-resonance happens because a real inductor stops acting like an inductor above a certain frequency. There is capacitance, on the order of picofarads, between the turns of copper wire. An ideal inductor in a schematic is pure inductance. A real one also has winding resistance, plus inter-winding capacitance in parallel. At low frequencies the part acts as an inductor. At higher frequencies the parallel capacitance has lower impedance, and the part behaves more like a capacitor. In the amplifier circuit, the inductor must not self-resonate anywhere in the signal's frequency band.
Solenoid vs. Conical: A Qualitative Comparison
The presenter compares the two types qualitatively. In an ordinary solenoid, every turn has nearly the same diameter and pitch. So the parasitic capacitance between turns is almost uniform. The whole coil behaves as one LC resonant circuit, self-resonates at a particular frequency, and stops working as an inductor above it.
For why the conical form works over a wider band, the presenter says there are several explanations. One is that each turn has a different inductance and a different inter-winding capacitance, which spreads the resonance points out. Another is that the sections of the coil, from the narrowest diameter to the widest, each handle a different frequency band. Either way, the presenter says, the defining feature of a conical inductor is that it keeps acting as an inductor over a wide frequency range.
The Experiment: A Handmade Conical Inductor on a NanoVNA
To test this, the presenter wound a conical inductor by hand and placed it in a circuit configured as a bias tee, like the one in the amplifier example. The circuit was connected to a NanoVNA to measure S-parameters. The sweep ran from 50 kHz to 900 MHz, with the vertical axis in dB.
The presenter describes the two parameters briefly:
- S11 shows how much of the signal is reflected. Here, lower dB is better, since you don't want a signal you put in to come back.
- S21 shows how well the signal gets from the input port to the output port. Ideally it stays as close to 0 dB as possible everywhere except DC, meaning the signal passes through without attenuation.
Conical Inductor Results
At low frequencies, the inductor's impedance is low. The signal line is effectively connected to ground through only the winding resistance, almost a short circuit. The signal is reflected partway along the line, so S11 rises. It is also attenuated before it reaches the output, so S21 falls at the low end.
At 837 MHz, something happens: S11 rises and S21 drops. The presenter interprets this as the inductor's impedance falling there, possibly because the inter-winding capacitance causes a series-resonant behavior. Near this frequency, input signals are reflected back and the output is attenuated.
There does appear to be a resonance point there. The presenter thinks the part may still act as an inductor above it. They wanted to look at higher frequencies to find the next resonance, but they had no network analyzer that reaches tens of gigahertz, so they left it for now. They added a light request to measuring-instrument manufacturers.
Solenoid Inductor Results
For comparison, the presenter measured an ordinary solenoid inductor with a similar diameter and nearly the same number of turns as the conical one. They said this result was not what they expected, and the conical inductor's characteristics might be the weaker of the two.
At low frequencies, the solenoid's inductance can be larger than the conical coil's, so its low-frequency drop seems smaller. There appear to be resonance points around 350 MHz and 550 MHz, where S21 dips. The dip is only about 0.5 dB, which the presenter judges fine for practical use. The solenoid showed no S21 drop near 840 MHz, where the conical inductor had one. Up to 900 MHz, the presenter concludes, the solenoid looks like the better performer.
Conclusion: The Broadband Advantage Wasn't Confirmed
The presenter notes that the reason to use a conical inductor is to keep inductor behavior over a wide band. Within the 900 MHz range measured here, they could not confirm the conical coil's broadband advantage. They attribute this to both the measurement setup and the build: it was not the conical inductor they had hoped for.
They also found the coil quite hard to wind. They would like to try different winding methods and taper ratios, and to run the test again once they have equipment that can measure at higher frequencies. The question of whether a well-made conical inductor beats a solenoid above 900 MHz remains open.
This video is brought to you courtesy of DigiKey. Hello. Today we will look at this strangely shaped inductor. This is called a conical inductor. Conical means cone-shaped. As the term implies, the inductors are conical in shape. I'm sure there are not many people, even those who work in electronic circuit design, who have seen conical inductors or actually used them. Both normal and conical inductors operate as inductors, but we'll see what benefits come from this shape.
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First, here is the conical inductor. Common inductors are wound into a solenoidal shape like this, use concentrated windings, or are wound on core material such as ferrite cores. The reason why this inductor is shaped this way is to widen the frequency band over which it operates as an inductor. I will explain it while looking at examples of circuits where it might actually be used.
For example, consider a high-frequency amplifier with this configuration: RF input from the left, a transistor, and RF output. The actual circuit doesn't work with just a signal source and transistors. A circuit and power supply to bias the transistor with DC are required. Naturally, capacitors are connected to the power supply line for smoothing and grounding noise from the power supply.
Here's what I'm wondering: what happens if we connect such a power supply directly to the transistor to bias it? Let's try it out and connect the power supply directly to the transistor. First, let's look at it from a DC perspective. The transistor seems to be biased without any problems. And what happens to the AC signal? There is a high-frequency input through the capacitor, connected to the transistor and this power supply section.
Now let's look at the capacitor connected to the power line. The higher the frequency, the lower the capacitor's impedance. So the high-frequency signal will flow toward the bypass capacitor instead of the transistor. Then we haven't been able to amplify the signal with this transistor. Even if we could, the gain is likely to be low.
Now we've seen it from the RF signal side. Let's consider what happens when we look at it from the power supply side as well. Assuming there is noise from the power supply, noise components not removed by the capacitor here are transmitted to the transistor side. They might be amplified by the transistor, and the noise components may be transmitted to this RF signal side. As we have seen so far, connecting directly to the power supply might allow us to bias the transistor, but signal amplification seems difficult.
Let's put the inductor back in here and think about it again. Since the inductor conducts direct current, the transistor bias seems to be working fine. What happens to RF signals from a signal source? Since the inductor has a high impedance for AC signals, the signal doesn't go to the inductor. Therefore, high-frequency signals can go to the transistor, and it looks like we could amplify the signal properly.
We have just looked at the input side of the circuit. The circuit on the output side also contains an inductor. If there is an inductor in this area, the amplified high-frequency signal won't flow to this side and can flow properly to the RF output. Incidentally, a circuit combining inductors like this one with capacitors for DC blocking is called a bias tee.
Can we use any inductor in this part? Not exactly. It depends on what frequency this amplifier operates at. If the amplifier is designed to work over a wide bandwidth, the inductor must operate as an inductor over a wide frequency bandwidth, and its self-resonant frequency must be as high as possible. More precisely, it is better to say that we should design the inductor so that there are no self-resonant frequencies among the operating frequencies.
Here's the term "self-resonant frequency." Depending on the frequency, inductors will actually stop operating as inductors. This is because there is capacitance on the order of picofarads between the copper-wire windings. In a schematic, the ideal inductor has only the L component. The actual inductor has winding resistance and capacitance between the windings in parallel.
In the low-frequency range, it acts as an inductor. At some higher frequency range, the impedance of the capacitor becomes lower, and it actually works like a capacitor. In the previous circuit, it is important that these inductors do not self-resonate in the signal's frequency band.
From here, we can talk qualitatively. We will look at the differences between normal solenoid inductors and conical inductors. In a normal solenoid inductor, the diameter and pitch of each turn are nearly uniform. Therefore, the parasitic capacitance between the windings is almost uniform. The entire coil behaves as a single LC resonant circuit. As a result, it will self-resonate at a certain frequency. At higher frequencies, it will no longer function as an inductor.
There are several ways to look at why conical inductors, on the other hand, work over a wide bandwidth. One is that the inductance values and capacitance between windings differ for each turn, dispersing the resonance points. Another view is that the sections from the smallest diameter to the largest each handle different frequency bands. In any case, the characteristic of conical inductors is that they continue to operate as inductors over a wide frequency range.
Now let's check how broadly the conical inductor actually works. Here is a handmade conical inductor. It's wound like this. We will put this in the circuit. This time, it is intended to be used in a bias tee configuration, as in the previous amplifier circuit. I measured it with a circuit like this, connected to the NanoVNA, to measure the S-parameters.
Here are the measurement results. I'm looking at S11 and S21. The horizontal axis is frequency, from 50 kHz to 900 MHz. The vertical axis is in dB. I will not go into a detailed description of the S-parameters, but briefly, S11 indicates how much of the signal is reflected. In this case, basically, the lower the dB, the better. In other words, if you put a signal in, you don't want it to be reflected or returned.
S21 indicates how well the signal is transmitted from the input port to the output port. In this case, it is desirable to stay as close to 0 dB as possible, except at DC. That is, if you put a signal in, you want it to reach the output unchanged, without attenuation.
Looking at the results again, in the low-frequency range, the impedance of the inductor is also lower, so the signal input and ground are connected by the winding resistance of the inductor. The signal is reflected in the middle of the line, and S11 becomes larger. The inductor is effectively in a short-circuit state with almost no inductive impedance. The signal does not travel to the output but is attenuated along the way. As a result, S21 gets smaller at lower frequencies.
In the results, something is going on at 837 MHz. S11 is bigger, and S21 is smaller. Here, the impedance of the inductor is lower. Capacitance between the windings may cause series-resonant operation. In other words, around this frequency, input signals are reflected back, and by the time they come out of the output port, they are attenuated and reduced in amplitude.
These results show that there is certainly a resonance point in this area, but it seems to work as an inductor even beyond that. I would like to look at higher frequencies until the next resonance point becomes visible. I didn't have a network analyzer that can measure up to tens of GHz, so we decided not to do so at this time. We are looking forward to working with you, measuring instrument manufacturers!
Next, we'll look at the results for a normal solenoid inductor. Its diameter is similar to the conical inductor's, and the number of turns is almost identical. Apparently, the results suggest that the characteristics may not be good. First, let's look at the low-frequency range. Compared to the conical inductor, the inductance value can be larger. Therefore, there seems to be less of a drop in low-frequency characteristics.
I see what look like resonance points at 350 MHz and 550 MHz. S21 has declined a bit. It is about 0.5 dB, so it seems to be fine for practical use. There is no drop in S21 near 840 MHz, as there was with the conical inductor. Looking at this, the solenoid seems to give a better result in the range up to 900 MHz. The purpose of using conical inductors is to have them work as inductors over a wide bandwidth, but at least in the band up to 900 MHz measured this time, the conical inductor's broadband advantage could not be confirmed.
Today, I have briefly explained what a conical inductor is, with experiments. Because of issues with the measurement system and manufacturing, the conical inductor did not turn out as I had hoped. I hope you understand the principle of operation of conical inductors and why they can be used over a broad bandwidth.
I actually tried winding a conical inductor this time, and it was quite difficult to make. You can try different winding methods and taper ratios. When the setup is ready to measure at higher frequencies, I would like to try again!
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