N2VY: 500 Watt Antenna Tuner Part 4B Inductor Design

One of the design challenges that Jeff, K6JCA outlines in his blog is stray inductance of the connecting wires or PCB tracks. He used hand wiring in his construction, so I thought I might do better with a PCB layout. I went through a design cycle with six air wound inductors and two powdered iron core inductors and did a few design iterations of the PCB with KiCad. I did not build the board but extracted the board geometry and estimated the path inductance. My results were the same as Jeff's.

I decided to build all my inductors with toroid cores. This provides me the advantage of packing them closer to each other and help keep the connecting tracks shorter and hence reduce the path inductance. This is the approach that some of the commercial high power antenna tuners take.

Also, I noticed that some of the commercial high power antenna tuners placed the capacitor and inductor relays on the back side of the board. This approach tends to further reduce the path inductance without increasing the PCB cost since I am using through hole relays and calling for solder mask on both sides of the board. Preliminary estimate puts the track inductance at 25 nH. I will explore if I can leave off the 25 nH inductor and when the tuning calls for it, just rely on the track inductance.

For high power inductors, the recommended material to use is powdered iron cores (not ferrite), so that is what I will use.

The Mini Ring Calculator for Mac is now available, but I am familiar with the Micrometals on line tool, so, that is what I will use. I will assume an internal enclosure temperature of 50 degrees C and maximum core temperature increase of 50 degrees C. That meets the maximum toroid core temperature of 100 degrees C which is fine for intermittent use. The other factor that I need is the maximum RMS current through the inductor at each frequency.

My simulator (described earlier), calculates maximum current through the inductors and maximum voltage across the inductors, but not the current at maximum voltage. Fortunately, knowing the maximum voltage, I can calculate the current at this voltage with a spreadsheet.

The following table is the simulator output that shows peak inductor currents and peak inductor voltages across the HF bands at average 200 watts operating power.

	Ind Current	12.8 uH	6.4 uH	3.2 uH	1.6 uH	800.0 nH	400.0 nH	200.0 nH	100.0 nH	50.0 nH	25.0 nH
160m low	8.9	467	442	298	161	81	40	20	10	5	3
160m high	8.9	0	458	322	178	90	45	22	11	6	3
80m low	8.9	0	474	437	292	157	78	39	20	10	5
80m high	8.9	0	0	458	322	178	90	45	22	11	6
40m low	8.9	0	0	474	437	292	157	78	39	20	10
40m high	8.9	0	0	453	444	301	163	82	41	20	10
20m low	8.9	0	0	0	474	437	292	157	78	39	20
20m high	8.9	0	0	0	466	440	297	160	80	40	20
17m low	8.9	0	0	0	0	468	351	200	101	51	25
17m high	8.9	0	0	0	0	471	351	201	102	51	25
15m low	8.9	0	0	0	0	484	383	229	118	59	29
15m high	8.9	0	0	0	0	479	386	233	120	60	30
12m low	8.9	0	0	0	0	481	415	265	139	70	35
12m high	8.9	0	0	0	0	483	417	266	140	70	35
10m low	8.9	0	0	0	0	474	437	291	157	78	39
10m high	8.9	0	0	0	0	472	446	305	166	83	42
6m low	8.9	0	0	0	0	0	483	417	266	140	69
6m high	8.8	0	0	0	0	0	476	433	283	150	75

Max	8.9	467	474	474	474	484	483	433	283	150	75
Max RMS	6.3	330.2	335.2	335.2	335.2	342.2	341.5	306.2	200.1	106.1	53

Inductor Maximum Peak Currents and Voltages Table

Here is the calculated RMS current through each inductor at the maximum voltage across that inductor at a given frequency.

	3.2 uH	1.6 uH	800.0 nH	400.0 nH	200.0 nH	100.0 nH	50.0 nH	25.0 nH
160m low	5.82	6.29	6.33	6.25	6.25	6.25	6.25	7.50
160m high	5.66	6.26	6.33	6.33	6.19	6.19	6.75	6.75
80m low	4.39	5.87	6.31	6.27	6.27	6.43	6.43	6.43
80m high	4.03	5.66	6.26	6.33	6.33	6.19	6.19	6.75
40m low	2.38	4.39	5.87	6.31	6.27	6.27	6.43	6.43
40m high	2.18	4.28	5.80	6.28	6.32	6.32	6.17	6.17
20m low	-	2.38	4.39	5.87	6.31	6.27	6.27	6.43
20m high	-	2.28	4.31	5.82	6.27	6.27	6.27	6.27
17m low	-	-	3.62	5.44	6.19	6.26	6.32	6.19
17m high	-	-	3.65	5.44	6.23	6.32	6.32	6.19
15m low	-	-	3.24	5.13	6.14	6.32	6.32	6.22
15m high	-	-	3.14	5.06	6.11	6.30	6.30	6.30
12m low	-	-	2.72	4.69	5.99	6.28	6.33	6.33
12m high	-	-	2.72	4.69	5.99	6.30	6.30	6.30
10m low	-	-	2.38	4.39	5.85	6.31	6.27	6.27
10m high	-	-	2.24	4.22	5.78	6.29	6.29	6.37
6m low	-	-	-	2.72	4.69	5.99	6.30	6.21
6m high	-	-	-	2.48	4.51	5.90	6.25	6.25

Inductor RMS Current at Maximum Inductor Voltage

As it can be seen from this table, in many instances the inductor current at maximum inductor voltage is the same or near the maximum inductor current value of 6.3 amps. But in some cases, especially for the higher value inductors, the current is much less than the maximum inductor current. Here is a table of all the cases where a lower inductor current value can be used.

	3.2 uH	1.6 uH	800.0 nH	400.0 nH	200.0 nH	100.0 nH
160m low	5.82
160m high	5.66
80m low	4.39	5.87
80m high	4.03	5.66
40m low	2.38	4.39	5.87
40m high	2.18	4.28	5.80
20m low	-	2.38	4.39	5.87
20m high	-	2.28	4.31	5.82
17m low	-	-	3.62	5.44
17m high	-	-	3.65	5.44
15m low	-	-	3.24	5.13
15m high	-	-	3.14	5.06
12m low	-	-	2.72	4.69	5.99
12m high	-	-	2.72	4.69	5.99
10m low	-	-	2.38	4.39	5.85
10m high	-	-	2.24	4.22	5.78
6m low	-	-	-	2.72	4.69	5.99
6m high	-	-	-	2.48	4.51	5.90

Cases With Less Than 6.3 A RMS Maximum Current

I spent a bunch of time playing around with different powdered iron cores to find the smallest ones that met my design criteria. After finding the ones that did meet my requirements, I tested the next smaller size and in all cases, they failed to meet the temperature rise criteria. This table is the outcome of this step. I should also note that I was using 12 AWG wire as the wire input parameter to the program.

The first inductance value is the design target. But given the AL values (see below) and an integer number of turns, only certain inductance values can be realized. The second inductance value is the estimated value based on the core properties (AL value). After these inductors are built and tested, I will list their actual values.

L (nH)	Core	AL (nH/N2)	Turns	L (nH)	I (Arms)	f (MHz)	P (W)	T (deg C)
25	T94-17	2.9	3	26	6.3	30	1.7	33
50	T94-17	2.9	4	46	6.3	30	2.6	47
100	T130-17	4.0	5	100	6.3	30	4.7	49
200	T184-17	8.7	5	210	6.3	30	7.7	43
400	T184-17	8.7	7	410	6.3	7.3	3.4	22
400	T184-17	8.7	7	410	6.0	14.35	5.5	32
400	T184-17	8.7	7	410	5.5	21.45	7.0	39
400	T184-17	8.7	7	410	4.7	30	7.0	42
800	T184-17	8.7	10	850	6.3	7.3	6.1	35
800	T184-17	8.7	10	850	4.4	14.35	5.2	31
800	T184-17	8.7	10	850	3.7	18.2	4.6	28
800	T184-17	8.7	10	850	3.3	21.5	4.4	27
800	T184-17	8.7	10	850	2.8	30	4.8	29
3200	T184-17	8.7	14	1660	6.0	4	6.4	36
3200	T184-17	8.7	14	1660	4.4	7.3	5.0	31
3200	T184-17	8.7	14	1660	2.4	14.35	2.6	18
3200	T184-17	8.7	20	3310	4.4	4	2.3	20
3200	T184-17	8.7	20	3310	2.4	7.3	3.0	17

Inductor Design Using 12 AWG Wire

The parameter AL needs an explanation. The formula for the number of turns from the RF design book is:

\begin{equation}N = 100 \times \sqrt {\frac {L}{A _{L}}}\end{equation}

Where N is the number of turns and L is inductance in micro Henries, N in turns and AL in micro Henries per hundred turns squared.

Important to note that Amidon publishes its AL values in micro Henries per 100 turns squared while Micrometals publishes them in nano Henries per turns squared. So, while using the Micrometals data, drop the 100 in the formula and use nano Henries for L.

It is worth mentioning that 2 and 6 material that could potentially be useful in this application have much higher AL values for their larger cores that can support the required power levels. These higher AL values make it much harder to get close to the desired inductance values with any accuracy.

I built a few of these inductors and the inductance was not anywhere near what I expected. To simplify the task of experimenting and finding out what is going on, I switched to 22 AWG magnet wire (working with 12 AWG wire is very yard). The graph below is a plot of the AL value vs. the measured inductance for a T187-17 core which has a specified AL value of 8.7 nH per turns squared.

Toroid AL value vs. Measured Inductance

It is clear from the graph that for smaller inductors (less turns), the wire inductance dominates. But as the number of turns increase since the AL value changes with the square of the number of turns, we asymptotically approach the specified AL value.

After my experience with 12 AWG wire (which I had picked when I was going to use air core inductors), I decided to consider a thinner gauge wire since using a toroid allowed me to use less turns. I experimented with a number of different wire gauges and 18 AWG wire seemed to meet the power loss requirements well. I built a number of inductors to the exact number of turns predicted by the formula (and the design tool), tested them and then took off the turns needed to obtain the required inductance. Below is a plot of designed turns vs. the experimental turns.

Measured Turns vs. Calculated Turns

Armed with this data, I was ready to run through the design process. In the first iteration, I used the same turns as the table with the 12 AWG wire and recorded the result. But then I reduced the turns ratio according to the above graph equation as follows:

L (nH)	Core	Designed Turns	Measured Turns
25	T94-17	3	1
50	T94-17	4	2
100	T130-17	5	3
200	T184-17	5	3
400	T184-17	7	4
800	T184-17	10	8
1600	T184-17	14	12
3200	T184-17	20	18

Specific Inductance Calculated and Measured Turns From the Graph

With these new number of turns, I calculated the power loss in the core. What is significant in this table is the number of turns (taken from the above table) and the power dissipation (P) and temperature rise (T). I have intentionally left off the 25 nH inductor from this list in the hope of using the PCB trace inductance in is place.

L(nH)	Core	AL (nH/N2)	Turns	L (nH)	I (Arms)	f (MHz)	P (W)	T (deg C)
50	T94-17	2.9	1	46	6.3	30	0.7	18
100	T130-17	4.0	2	100	6.3	30	1.5	36
200	T184-17	8.7	3	210	6.3	30	5.3	35
400	T184-17	8.7	5	410	6.3	7.3	3.6	25
400	T184-17	8.7	5	410	6.0	14.35	5.2	34
400	T184-17	8.7	5	410	5.5	21.45	6.0	38
400	T184-17	8.7	5	410	4.7	30	5.9	38
800	T184-17	8.7	8	850	6.3	7.3	6.6	42
800	T184-17	8.7	8	850	4.4	14.35	5.1	33
800	T184-17	8.7	8	850	3.7	18.2	4.4	29
800	T184-17	8.7	8	850	3.3	21.5	4.0	27
800	T184-17	8.7	8	850	2.8	30	4.0	28
1600	T184-17	8.7	12	1660	6	4	7.0	44
1600	T184-17	8.7	12	1660	4.4	7.3	5.4	35
1600	T184-17	8.7	12	1660	2.4	14.35	2.6	19
3200	T184-17	8.7	18	3310	4.4	4	6.6	41
3200	T184-17	8.7	18	3310	2.4	7.3	2.8	20

Power Dissipation and Temperature Rise for the Designed Inductors

What remains is the building and testing of the inductors. Here is the test data (I have intentionally left out the 25 nH inductor in the hopes of using the PCB trace inductance in its place):

L (nH)	Turns	3 MHz	5 MHz	7 MHz	14 MHz	30 MHz
50	1	44.6			44.8	44.9
100	2	107	100	100		101
200	3	239			240	246
400	5	414			420	440
800	8	805			831	929
1600	12	1568	1576	1590	1670
3200	18	3170	3211	3275

Inductance Value Measured at Various Frequencies

It is worth noting that the apparent inductance of the toroids increasing with frequency is the effect of the stray parallel capacitance of the wires. It is not very noticeable with fewer turns and as the number of turns increases so does the stray capacitance.

And finally, here is a picture of the inductors: