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Intermodulation in Broadband Transformers

In developing preamplifiers with high intermodulation performance, it's necessary to look at all aspects of the design, including coupling transformers. To illustrate the difference in intermodulation performance, I built and tested eight 1:1 broadband transformers today. There's a considerable difference between the worst and best transformers, although all have quite reasonable insertion loss and bandwidth.

This page is not intended to be an exhaustive analysis of alternative transformer designs, but  rather measures the performance of a set of eight "typical" transformers found in amateur radio designs. (As explained later, due to anomalies with one transformer, a second version was built and  tested.)

Revision History
22 June 2010 Original release
23 June 2010 Updated data on 75 material core intermodulation
03 July 2010. Added data for CoilCraft and Mini-Circuits transformers

The transformers are pictured below. (The photo shows a 9th transformer at the lower right that is not discussed.) Five are wound on multi-aperture (binocular) cores and four are on toroid (ring) cores. Ferrite types include Fair-Rite 43, 73 and 75 and 35 material from the Steward unit of Laird Technologies. All transformers have the same number of turns on the primary and secondary.
 

 

ID Turns and Wire Type (each winding) Core Type Comments
BN73-01 7 turns No. 30 magnet wire BN73-202 Relative permeability 2500
BN73-02 7 turns No. 24 magnet wire BN73-202 Relative permeability 2500
BN73-03 1 turn No. 24 magnet wire BN73-202 Relative permeability 2500
BN73-04 1 turn RG-316 Teflon coaxial cable BN73-202 Relative permeability 2500
BN43-01 3 turns No. 24 magnet wire BN43-202 Relative permeability 850
35T-01 14 bifilar turns no. 26 magnet wire 35T0501-10H The 35T0501 core is slightly larger than a FT50-series core, and is thicker. Relative permeability is 5000.
FT43-01 14 bifilar turns no. 26 magnet wire FT50-43 Relative permeability 850
FT75-01 14 bifilar turns no. 26 magnet wire FT50-75 Relative permeability 5000
FT75-02 14 bifilar turns no. 30 wire-wrap wire FT50-75 Relative permeability 5000; re-tested due to problems with FT75-01 intermodulation anomalies.

My choice of cores is based upon material and types commonly used in amateur radio applications, and, with respect to the Steward 35T0501-10H product, a core used in several Clifton Radio products.

The transformer designs fall into two groups:

General coverage; from frequencies of a few KHz up to 50 MHz

  • BN73-01
  • BN73-02
  • 35T-01
  • FT43-01
  • FT75-01 (and FT75-02)

Amateur Radio coverage; from 1 MHz to 50 MHz

  • BN73-03
  • BN73-04
  • BN43-01
My general coverage transformers are designed with a magnetizing inductance of at least 200 ohms at 50 KHz, while the amateur radio transformers are at least 200 ohms at 1 MHz. I won't go over RF transformer design in detail here, as the subject is well covered elsewhere, but will note that the usual design criteria sets the magnetizing inductance to provide an inductive reactance at least four times the driving or load impedance. Since these transformers work at 50 ohms, source and  termination, the inductance of each winding should be at least 200 ohms at the 50 KHz for general coverage or 1 MHz for amateur radio coverage.

The number of turns required for 200 ohms reactance at the target frequency can be computed by reference to the manufacturer's catalogs, or by the handy on-line calculator at http://www.kitsandparts.com/toroids.php - click on the core type and a new page appears with a calculator at the bottom. Enter the frequency and required reactance in ohms and the number of turns required for the selected core and the winding length in inches is calculated. There's also an expanded version of this program available for downloading and installation on a Windows PC at http://www.kitsandparts.com/tcalc.html. It's easy to expand the core types in this program's database by editing its associated INI file, by the way.
 

The measured upper and lower -3 dB points, the mid-band insertion loss (measured at 1 MHz) and a link to frequency response plot appear in the table below. The swept frequency plot runs from 5 KHz to 50 MHz and has a log frequency (horizontal) axis.

 

ID Lower -3 dB Frequency Upper 3 dB Frequency Mid Band Insertion Loss (dB) Click in the box below for enlarged frequency response plot
BN73-01 6 KHz > 50 MHz 0.07
BN73-02 6 KHz > 50 MHz 0.06
BN73-03 270 KHz > 50 MHz 1.6
BN73-04 275 KHz > 50 MHz 1.6
BN43-01 200 KHz > 50 MHz 0.3
35T-01 5 KHz > 50 MHz 0.07
FT43-01 43 KHz > 50 MHz 0.07
FT75-01 5 KHz > 50 MHz 0.14
FT75-02 5 KHz > 50 MHz 0.09

 

I then measured the 2nd and 3rd order intermodulation intercept (output) of the eight transformers. The general protocol used can be viewed by clicking here. Test tones of 3007 and 4011 KHz are applied to the device under  test, with the drive level set to provide 0 dBm output. Second order intermodulation products are found at 1004 and 7018 KHz, and third order products at 2003 and 5015 KHz.

I've extended the measurement range of this setup, however, by adding a deep 3 to 4 MHz notch filter between the device under test and the spectrum analyzer. To ensure the device under  test is properly terminated, a 20 dB attenuator is installed between the D.U.T. and the notch filter. Adding the notch filter permits the HP 8568B spectrum analyzer to operate at maximum sensitivity without significant instrument-based intermodulation artifacts.

The table below provides the output intercepts in dBm for the instrument setup and for the transformers.
 

Freq KHz Instrument Limit BN73 01 BN73-02 BN73-03 BN73 04 BN43-01 35T-01 FT43-01 FT75-01 FT75-02
1004 113.1 111.0 111.9 103.0 103.2 111.2 113.1 112.1 102.9 111.3
2003 57.7 57.7 57.7 44.5 44.8 42.2 57.7 55.1 40.6 57.7
5015 58.6 58.6 58.6 55.4 55.1 47.6 58.6 58.6 41.4 58.6
7018 114.2 105.2 106.8 98.6 98.5 103.3 110.7 109.1 108.6 105.9

I've shaded in green measurements that are limited by the instrumentation floor. Four transformers, have both third order intercepts un-measurable by my current test setup and a fourth transformer has one third order product at the instrument floor.

None of the transformers show both second order intercepts at the instrument limit, although the 14 turn transformer wound on a Steward 35T0501 is instrument limited at 1004 KHz.

In general, the transformers wound with 7 turns on a BN73-202 core are excellent performers. However, the best performing transformer is 14 turns bifilar wound on a 35T0501-10H core, with three output intercepts instrument limited and the fourth intercept within 4.5 dB of the instrument floor.

The spectrum analyzer image below shows the 2003 KHz product level for four transformers. As  the plot shows, there's a striking difference between the best and worst transformers.

 

Perhaps the more interesting questions are why certain of these transformer designs are so poor. In particular the low turn transformers wound on both 73 and 43 material binocular cores and the 14 turn bifilar transformer on a 75 material core.

There are two different effects at work here.

 


Consider first the binocular core  transformers designed for amateur radio bands. The BN73-03 and -04 designs have but one turn and the BN43-01 design has three turns. The much better performing BN73-01 and -02 designs have seven turns. Since inductance is proportional to the square of the number of turns for the same core dimension and material, the seven turn transformers have 49 times the inductance and hence inductive reactance compared with the one turn versions.

But, at the 3 and 4 MHz  test tones, both the single and seven turn transformers have more than enough inductance to make negligible the reactance of the shunting magnetizing inductance.

But, that's not the end of the analysis.

The classic transformer flux equation is: 

Bac is the AC flux in Teslas,
f is frequency in Hz,
E is AC voltage in volts,
Ac is core effective area in cm2,
K is a constant and
N is the number of turns.

Hence as N increases, Bac decreases for a constant applied AC voltage. Since the transformers under test are measured at 0 dBm and 50 ohms impedance, the applied voltage is identical for all eight transformers. (Actually, the applied voltage is slightly greater for transformers with higher loss since the 0 dBm power level is measured at the output winding.) Accordingly, the single turn BN73-03 and -04 transformers will have seven times as much AC flux as does the seven turn BN73-01 and -02 designs.  Transformer distortion is proportional to flux, so it makes sense that the single winding transformers will have greater intermodulation distortion and hence lower 2nd and 3rd order intercepts.

Another way to look at this is that for a constant AC voltage, the AC, Iac, current through the magnetizing inductance is proportional to 1/XL, the inductive reactance. Flux (whether AC or DC) is proportional to N * I. But the inductance, and, of course, XL, proportional to the square of the number of turns. Bac is proportional to N*Iac. But Iac = E/XL so Bac is proportional to N * E / XL But XL is proportional to the square of the number of turns. Hence Bac is proportional to N * E / N2. Cancel the extra N and Bac is proportional to E/N.

 

With respect to the bifilar wound FT75-01 transformer, I suspected a problem. It should behave similarly to the 35T-01 transformer, as the  two cores have similar permeability. Although the frequency response is similar, there's a huge difference in intermodulation performance.

There is a significant physical difference between the 75 and 35 cores, however. The Fair-Rite 75 core is "unfinished" in the sense that it is uncoated and has only minimal edge smoothing. In contrast, the Steward 35 material core has been tumbled and coated. It has smooth edges and the ferrite body is coated with an insulating material. This physical difference is important because ferrites are hard and abrasive. It's unfortunately all too easy to abrade the enamel insulation on the magnet wire when winding the transformer on an unfinished core.

As I said on this page originally "It's possible that one of the wires has damaged insulation and is coupling electric field energy to the core ... I'll wind another transformer with Kynar insulated wire and see if the same intermodulation performance is observed."

I've done that and the intermodulation performance of the Kynar insulated transformer, ID FT75-02, is excellent. Close observation of FT75-01 revealed several places where bare copper could be seen. At least one of these bare patches must have contacted the core, placing a combined electric and magnetic field in the core.

Interestingly, there is little difference in frequency response between the transformer wound with damaged insulation and the Kynar insulated transformer. The damaged insulation transformer has a bit greater loss at mid-band, but less loss at higher frequencies. The high frequency difference would well be due to insulation dielectric loss.

In any event, it pays to be careful when winding a transformer or inductor on an unfinished ferrite core. Either insulated wire should be used, or the core should be coated or wrapped with thin Teflon tape.

Coilcraft and Mini-Circuits Transformers

Coilcraft and Mini-Circuits are two manufacturers of wide band RF transformers and I measured the frequency response and intermodulation performance of a small sample from each manufacturer. A few of the measured transformers are shown below, along with one of the home made transformers wound on a BN-73-202 core. In addition, a home made transformer wound on a small core is shown second from the left. The transformers are equipped with 0.1 inch space pin headers for quick connection to test equipment.
 


Seven commercial transformers and one additional home made transformer were evaluated:

Model Number Manufacturer Impedance Ratio
ADT-1-6T Mini-Circuits 1:1
T1-6T Mini-Circuits 1:1
WB1010 Coilcraft 1:1
WB1010-1 Coilcraft 1:1
T2-1T Mini-Circuits 1:2
WB2-1TLS Coilcraft 1:2
WB2-1T Coilcraft 1:2
35T-02 Homebrew 1:1
1:1 Impedance ratio transformers are evaluated directly. 1:2 Ratio transformers are evaluated "back-to-back." Two transformers of each model are connected with the high impedance side together, and the low impedance side used as input and output. Since the two transformers in series are identical, the insertion loss can be assumed to be equal and hence the insertion loss of a single transformer is one half of the pair. Intermodulation measurements use the same methodology. However, there's no simple way to accurately allocate the intermodulation products to one transformer. Hence intermodulation data is presented for the series pair, without adjustment.

The 3.007 MHz and 4.011 MHz test signals are adjusted to a level of 0 dBm for each test tone at the transformer's output. For loss loss transformers, the input and output test signals are essentially identical, within a couple tenths of a dB or so. The series connected 1:2 transformers, however, have an appreciable loss, around 1.5 dB. Hence, the transformer on the input side is driven with a signal at +1.5 dBm. In theory, therefore, intermodulation products generated in this transformer of the pair will be greater than those generated in the transformer nearest the output.

The table below presents the output intercepts, 2nd and 3rd order, for the seven Coilcraft and Mini-Circuits transformers.
 

Freq KHz OIP Order ADT-1-6T T1-6T WB1010 WB1010-1 T2-1T WB2-1TLS WB2-1T
1004 OIP2 108.5 112.6 107.8 95.9 77.2 98.1 99.9
2003 OIP3 57.7 57.7 57.7 54.6 43.4 40.0 40.7
5015 OIP3 58.6 58.6 58.6 58.6 45.2 41.4 43.8
7018 OIP2 108.3 109.7 105.5 94.5 80.6 101.7 96.2

Salmon shading identifies measurements that are limited by test equipment performance and hence values in these cells are minimum performance levels.

Blue shading indicates 1:2 ratio transformers, made with back-to-back connections.

In addition to intermodulation performance with 3 and 4 MHz test tones, I ran a second series of measurements with test tones of 883 and 1357 KHz to assess how the 1:1 Coilcraft and Mini-Circuits perform at frequencies typical of the AM standard broadcast (medium wave) band. In order to avoid artifacts from the HP8657A synthesized signal generators I use for these tests, as with the 3 and 4 MHz signals, the test signals are slightly offset from multiples of 10 KHz. In addition to Coilcraft and Mini-Circuits transformers, I also evaluated four home made transformers.

The 35T-01, BN-73-01 and FT-43-01 transformers are the ones described earlier. 35T-02 is new for this test. It consists of 10 bifilar turns of no. 32 AWG magnet wire wound on a Steward 35T0231 ferrite core. This is the small core (0.23 inches diameter) in the photograph above.
 

Freq KHz OIP Order 35T-02 35T-01 BN-73-01 FT-43-01 ADT-1-6T T1-6T WB1010 WB1010-1
409 OIP3 41.0 51.9 55.7 44.9 47.8 48.1 49.4 39.1
474 OIP2 115.3 111.9 115.3 115.3 115.3 115.3 115.3 99.4
1831 OIP3 50.9 57.7 58.7 49.1 56.2 56.4 58.7 48.8
2240 OIP2 112.0 113.4 112.4 109.1 110.5 111.8 113.8 99.7

At medium wave frequencies, the BN-73-01 transformer is the clear winner, with none of the Coilcraft and Mini-Circuits transformers coming close in 3rd order intermodulation intercept at 409 KHz. It is also an excellent performing design when the 3 and 4 MHz test tone products are examined.