Clifton Laboratories 7236 Clifton Road  Clifton VA 20124 tel: (703) 830 0368 fax: (703) 830 0711

E-mail: Jack.Smith@cliftonlaboratories.com
 

One project I've been occupied with, likely to be available as a kit or assembled unit, in the next few months, is an AM broadcast band rejection filter. My friend Ron, K8AQC, lives in a suburban Detroit location with extremely strong AM broadcast signals and this summer I built a one-off filter to pass frequencies below 400 KHz and above 1.8 MHz but to significantly attenuate signals in the 500-1700 KHz AM medium wave broadcast band.

The filter I built for Ron worked so well that I thought it might have use for others suffering from high level AM broadcast band signals. I've laid out a printed circuit board and have now assembled three filters and thought the design decision around inductor design might be of interest.

The figure below shows a near final schematic of the filter. I've made some small component value changes, but for the purpose of this discussion, the changes are not significant.

 

Material ID	Composition	Relative Permeability µr	Temperature Stability (ppm/°C)	Resonant Circuit Frequency Range (MHz)	Color Code
0	Phenolic	1	0	100.0 - 300.0	Tan
1	Carbonyl C	20	280	0.5 - 5.0	Blue
2	Carbonyl E	10	95	2.0 - 30.0	Red
3	Carbonyl HP	35	370	0.05 - 0.5	Grey
6	Carbonyl SF	8	35	10.0 - 50.0	Yellow
7	Carbonyl TH	9	30	5.0 - 35.0	White
10	Carbonyl W	6	150	30.0 - 100.0	Black
6	Carbonyl SF	8	35	10.0 - 50.0	Yellow
7	Carbonyl TH	9	30	5.0 - 35.0	White
10	Carbonyl W	6	150	30.0 - 100.0	Black
12	Synthetic Oxide	4	170*	50.0 - 200.0	Green/White
15	Carbonyl GS6	25	190	0.10 - 2.0	Red/White
17	Carbonyl	4	50	50.00 - 200.0	Blue/Yellow

Similar information for the common ferrite cores from the leading ferrite manufacturer, Fair-Rite, is provided below.
 

This is a lot of information—what do we make of it?

It should be apparent that our belief that no single material is suitable for the frequency range 10 KHz - 100 MHz is apparent in the data. But, do we really need a material that works uniformly over  this frequency range? Let's look at our filter circuit. (I'll provide high level arguments with limited math here—detailed mathematical circuit analysis will be left to the interested reader.)

One other point is that the discussion below suggests that the filter can be considered as independent series and parallel resonant circuits. That's a gross oversimplification if not an outright error, but has enough validity to make the exercise useful in understanding the choice of core materials.

At frequencies below a few MHz all the filter tuned circuits are operational. In the AM broadcast band, 530 - 1700 KHz the three parallel tuned circuits (L2, L4 and L6 with associated capacitors) should provide a high impedance path, whilst the four series tuned circuits (L1, L3, L5 and L7 and associated capacitors) form a low impedance path shunting this frequency range. The impedance (both parallel and series) is a function of resonant circuit Q (dominated by the inductors, since we can use polystyrene capacitors with very high Q) so we need all inductors to have high Q performance in this frequency range. The reject band depth is a function of the component Q.

Consider next what happens at relatively high frequencies, say 10 or 15 MHz up through 100 MHz or more. The parallel tuned circuits centered a round L2, L4 and L6 are way outside their resonant frequency range, and their impedance is dominated by the shunting capacitance. At 15 MHz, for example, the 2000 pF or so capacitors in this section of the filter have an impedance around 5 ohms. If L2, L4 and L6 are not particularly good inductors at these frequencies, there is only a small change in the impedance of these LC circuits. Hence, we can accept even a major drop in inductor performance of L2, L4 and L6 if required.

The four series tuned circuits associated with L1, L3, L5 and L7, however, must still retain a reasonably high impedance throughout the entire passband range. Otherwise, the desired signal frequencies will be shunted to ground and hence increased attenuation results. However, if these series resonant circuits collectively have an impedance of a few hundred ohms, the resulting passband loss may be acceptable. So we can accept some poorer performance of L1, L3, L5 and L7. (Remember as I mentioned at the outset, this is a grossly oversimplified analysis of how the filter actually works.)

In sum, therefore:

• At frequencies up to a few MHz, all seven inductors must provide good performance, high Q and  reasonably constant inductance with frequency.
• At higher frequencies, say above 10 MHz, we can accept some fall off of performance in L1, L3, L5 and L7.
• At higher frequencies, say above 10 MHz, L2, L4 and L6 can have rather significant performance impairments without harming our filter's overall performance.
• There's still a limit how bad all these inductors can be without excessive insertion loss, of course.

To help quantify these comments, we can look quickly at the math involved.

The impedance Z of a series RLC circuit such as the one shown at the right is:

where X_L is the reactance of inductance L at frequency f:

X_L = 2πfL

and X_C is the reactance of capacitor C at frequency f

X_C = 1/2πfC

R is the series resistance representing losses in the capacitor and inductor. If the capacitor's loss is small compared with the inductor's losses (as is quite often the case) the relationship between R and the inductor Q is:

R = X_L/Q or R = 2πfL/Q

At the  resonant frequency X_C = X_L, so Z reduces  to simply R. For a 2.5µH inductor, with a Q of 200 at 925 KHz, for example, R is 2*π *0.925x10⁶ * 2.5 x 10^-6 / 200 =  0.07 ohms.

In our filter design, the L1, L3, L5 and L7 circuits are resonant around 925 KHz, at which frequency X_C = X_L. At 10  times this frequency, or 9.25 MHz, X_L is 10 times as large as its value at 925 KHz and X_C is 1/10th its value. Returning to our equation for Z in terms of R, X_L and X_C, we note that (X_L - X_C) ≈ X_L, with sufficient engineering accuracy. The impedance Z is therefore:

Recasting this equation in terms of Q, we find:

which may be further simplified to:

This is an interesting result from which we may draw several conclusions, reinforcing mathematically my earlier observations:

• With a Q as low as 3, Z is within 5% of the value it has for infinite Q
• As Q diminishes, Z increases. Since the high frequency passband employs the series tuned circuit in shunt, increased Z is actually beneficial, not harmful, to the filter's loss.

Hence, at frequencies significantly above resonance, not all that important in determining the impedance of the series circuit. We could also extend this observation to note that even if the inductance drops with frequency due to changes in the core material's permeability with frequency, for example, Z may not change all that much. Of course, a radical change in inductance with frequency, such that the RLC circuit becomes resonant at some elevated frequency would be a problem.

A numerical example may help. Take the 2.5 µH inductor used in the earlier computation, but assume the Q drops to 20 at 9.25 MHz. What is Z?

• With Q=infinity, Z= 145.298 ohms
• With Q = 20, Z = 145.480 ohms

We can do the same analysis for the parallel resonant RLC network shown at the right, where the magnitude of the impedance is.

ω is the frequency in radians per second, ω=2πf where f is the frequency in Hz.

Amazing that moving one component makes such a difference in impedance complexity, isn't it? However, the equation is not as difficult to analyze as it might appear.
 

After all this work, which has taken me far longer to write than to consider during the design process, we conclude that:

• L2, L4 and L6 can be ferrite material, if the selected ferrite holds reasonably constant inductance up to 10 MHz or so (about 10 x the resonant frequency) and if the material's Q is reasonable over this range.
   
• L1, L3, L5 and L7 can be powdered iron, since they should retain reasonable Q well above 10 MHz.

Which ferrite and which powdered iron to use is the next question.
 

To obtain a sense of how these two core solutions work, I wound test inductors of approximately 14 µH:

• 15 turns, no. 24 AWG magnet wire on an FT50-61 core, nominal inductance at 2.5 MHz of 13.8µH, Q = 200 as measured on an HP 4342A Q-meter.
   
• 58 turns, no. 30 AWG magnet wire on a T50-7 core, nominal inductance at 2.5 MHz of 14.6 µH, Q = 184.
   
• 51 turns, no. 28 AWG magnet wire on a T68-7 core, nominal inductance at 2.5 MHz of 14.3 µH, Q = 220.

The figure below shows the variation in inductance of these three test coils over the range 800 KHz to 9 MHz, measured with an HP 4342A Q-meter. The 4342A is an analog instrument with a quoted accuracy of ±3% for inductance and ±7% for Q. At 15 µH, ±3% corresponds to ±0.45 µH, so it's reasonable to ascribe a great deal of the variation in the measured inductance up through 7 MHz or so as instrument error. (If the inductance is actually constant over this range, the observed instrument error is around ±0.9%.)
 

• T68-7: 1.25 pF
• T50-7: 1.38 pF
• FT50-61: 1.91 pF

The plot below shows the indicated Q for the three test inductors over the same frequency range. (No correction for distributed capacitance is made in the data.)

The type 61 ferrite material shows a considerable drop in Q with increased frequency, which again can be seen if the manufacturer's specifications are examined. The plot below is from Fair-Rite's catalog and shows how mix 61's "complex permeability" varies with frequency. For our purposes, I'll just say that the core material's intrinsic Q is the ratio of u'/u''. At 10 MHz, for example, Fair-Rite data shows u' is 125 whilst u'' is 2, providing an intrinsic material Q of 62. The "intrinsic Q" is, of course, degraded by copper loss in the winding and other considerations and therefore represents the maximum Q that one might observe.

To see how much effect the core material had on actual filter performance, I built three band reject filters, identical except for how L2, L4 and L6 were constructed. L1, L3, L5 and L7 in all three filters are wound on T50-7 cores.

• Filter 1: L2, L4 and L6 are wound on T50-7 cores
• Filter 2: L2, L4 and L6 are wound on T68-7 cores
• Filter 3: L2, L4 and L6 are wound on FT50-61 cores

The plots below show the measured response curves for the three filters, plotted onto single graphs. The difference between the three is negligible, amounting to fractions of a dB in the passband and, at most, a dB or two for a small portion of the reject band. Accordingly, the choice between FT50-61 and T50-7 or T68-7 cores for L2, L4 and L6 can be made on the basis of cost and convenience without concern over performance concerns.