Transcript
A Ferrite Loopstick For WWVB Reception Using The CME6005 Chip Emmett Kyle January 24, 2008 Abstract This document describes a practical approach in the design of a ferrite loopstick antenna for a radio controlled clock receiver that is tuned to the 60kHz station WWVB. This antenna connects directly to the Cmax CME6005 receiver chip. The main goals of this antenna design are to maximize signal recovery and produce an antenna that has a resonant resistance in the range of 40 − 100KΩ. According to the data sheet, this will provide the best possible signal to noise ratio for this chip. This is also a test for me to see what the capabilities of the LATEX typesetting and formatting tool can do, because trying to work with and display formulas with a regular word processor is like trying to “build a mnemonic memory circuit using stone knives and bear skins”[1].
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The Evaluation Board
The first antenna I built for WWVB reception was a 2’ diameter loop antenna. It works very well. This time around, I decided to try a ferrite loop stick antenna that mates with the CME6005 receiver chip. I happened to have a nice ferrite rod from a project I worked on many years ago. It is 0.75” diameter and 8” long. The CME6005 chip [2] is readily available at Digikey [3] and is fairly inexpensive. It along with a crystal are less than $5. They also sell preassembled receiver boards [4] which would be the best bet for most people, since the pin spacing on the chip is on 0.025“ centers. In other words, if you don’t have a stereo microscope to use when soldering it, you will more than likely have problems. The CME6005 is really easy to use since it only needs a few capacitors and a crystal to operate. It boasts 0.4µV sensitivity with a properly designed coil. Layout is fairly critical. The board I designed uses one side as a solid ground plane. (Figure 1). I also included two coupling capacitors for IN1 and IN2 so I could use the inputs without having to worry about clobbering the input bias if I wanted to connect my outside loop antenna or a signal generator.
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Figure 1: First coil and evaluation board
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The Coil Requirements
The sparse documentation for the CME6005 suggests that the resonant resistance value be somewhere in the range of 40 − 100KΩ. The data sheet doesn’t specify an optimum value, so I shot for the middle at 70KΩ. Actually from what I read, a resonant resistance of less than 40KΩ would have the amplifier noise dominate, while a resonant resistance greater than 100KΩ would have the L coil noise dominate. The resonant resistance of the coil is dependent on the C ratio and the coil Q. By matching it with the receiver input impedance, the optimum signal to noise ratio (s/n) can be achieved. The resonant resistance (Rres ) can be calculated by either one of these formulas: Rres =
1 2π(fh −fl )C
[5]
q L Rres = Q C [6]
where: fh = upper −3db frequency fl = lower −3db frequency f0 = center frequency C = capacitance L = inductance 0 Q = fhf−f l
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Trial And Error
The first coil I wound had a resonant resistance at about 400KΩ which was way too high. It had about 300 turns of 20/34 Litz wire on this core in two layers and had a self resonant frequency of about 90kHz. It became apparent that just going after the maximum signal recovery by slapping as many turns before self resonance was not going to get the best overall performance. The problem is that as you increase the inductance, the required capacitance becomes less, thereby increasing the resonant resistance since they are inversely proportional. The Q decreases as the inductance increases from more wire resistance and the increasing L/C ratio, which helps, but its hard to tell who ”wins the race“. Actually, the capacitance value will decrease in an inverse proprotion to the square of the number of turns and the decrease in Q would be fairly linear in proportion to the number of turns and the increasing L/C ratio, so the decreasing capacitance per number of turns will have the greatest impact to the resonant resistance for the most part. After winding and trying a few experimental coils, I also realized a couple more things. Using Litz wire gave Q values too high for good temperature stability and caused the resonant resistance to be above 100KΩ in the configurations I tried. However, using Litz wire is still the way to go because one ends up with less inductance per the number of turns. Therefore you can get more turns for the same inductance that you could with regular wire, and more turns equals more signal recovery. I solved the Q and Rres dilemma by ”dumping” some of the Q and putting the resonant resistance where I wanted it simply by adding about 9.4Ω of series resistance with the coil. This is a fairly low resistance, and it along with the wire resistance should only contribute about 5.78nV (section 5.6) to the input noise. The CME6005 data sheet suggested using a tuning capacitor in the range of 2.2nF - 6.8nF . The obvious value to shoot for would be the lower value since this would require more inductance and therefore more turns, and therefore more signal recovery.
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Figure 2: Final Coil and the PVC Housing. The two center “pucks” will hold the coil inside the tube once they are machined and have grommets installed.
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The Final Coil
The final coil ended up to be a single layer winding that covered most of the ferrite rod with about 3/800 − 1/200 free on the ends. (Figure 2) Coil Core Length Core Diameter Core Permeability Turns Wire AL value (100 turns) µe Cstray Cres D.C. resistance Inductance at 1kHz Inductance at 60kHz Q at 60kHz Q with 9.4Ωresistance Rres
Specifications 8.0” 0.75” Unknown 155 20/34 Litz wire 1.34mH 48.05 77.3pF 2.99nF 0.53Ω 2.65mH 2.35mH 237.2 71.8 67.67KΩ
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Finding The Unknown Coil/Core Parameters
You don’t really need specialized equipment to gather most of the information about an inductor in this frequency range. Only an oscilloscope with a 10x probe, an AC voltmeter with a db scale (you can use just the scope if you don’t have one and look for 0.707 amplitude), a signal generator, another coil or loop attached to the signal generator who’s self resonance is much higher than the frequencies you are working with. An LCR meter helps but is not required if you have some capacitors of a known value. A frequency counter connected to the signal generator is also very helpful in getting accurate measurements. Set up the two coils parallel, next to each other (but not too close) and connect the scope probe to the coil under test.
5.1
Calculation Of The Number Of Turns For A Desired Inductance When Using an Unknown core Material
Finding the AL value (inductance per number of turns) of an unknown core can be found by simply winding Ntest number of turns on the core and finding or measuring the resultant inductance. On a rod, it is preferable to wind the coil in the middle of the rod to obtain better accuracy of the measurement. Ntest should be at least 100 turns. Once the inductance is measured, it is easy to calculate the “ballpark” number of turns that will be required for the desired inductance: q desired Nturns = Ntest LLmeasured [7]
5.2
Stray Capacitance
There is a very useful formula for calculating the stray or distributed capacitance of an inductor. With this formula, all one has to do is take two measurements of the resonance frequency of the coil using two known capacitor values. The stray capacitance will equal: Cstray =
f22 C2 −f12 C1 f12 −f22
Final Coil Cstray f1 f2 C1 C2
[8] 77.3pF 56.45kHz 98.47kHz 3.30nF 1.03nF
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5.3
Finding The Inductance
Calculate the stray capacity of the coil and then add it to a known capacitor value. Use the known capacitor, find the resonant frequency and solve for L: L=
1 ω 2 (Cknown +Cstray )
[9]
where: L = inductance ω 2 = 4π 2 f 2 Cknown = A capacitor of a known value Cstray = stray capacity calculated in section 5.2 f = the resonant frequency
Some LCR meters do a pretty good job a giving true inductance, but they usually operate at 1kHz, so the inductance may be different at frequency of interest due to the core characteristics, skin effect, etc.
5.4
Finding The Effective Permeability (µe )
I did not know the initial permeability of the ferrite material I had, so I couldn’t calculate the effective permeability. Even if I did know the initial permeability, other factors like the winding geometry, etc. will give you a coil inductance that doesn’t match up to what would be calculated even if the permeability was known. One really doesn’t need to know the effective permeability unless you are interested in determining the signal recovery and or the signal to noise ratio of the coil. I thought it would be interesting to know these things, so I ended up winding an air core coil of the same dimensions as the ferrite version and determed its inductance. I then divided the inductance of the ferrite coil by the inductance of the air core coil. In the case of the final coil: µe = 2.35mH/48.93µH = 48.05
5.5
Signal To Noise Ratio And The Noise Floor
The signal to noise ratio (s/n) of a tuned loop is given by: q 0 √ Aµe Qf (s/n)(db) = 20log( 66.3N L e) [10] ∆f
The noise floor of the coil would then be: q L nf = 66.3N1 Aµe ∆f Qf0 [11] where: nf = noise floor volts N = number of turns A = cross sectional area in square meters µe = effective permeability 6
Q = the coil Q f0 = center frequency L = inductance volts e = field strength in meter ∆f = -3db bandwidth of the receiver Final Coil s/n 46.2db nf 0.492µV N 155 A 304.3x10x−6 m2 f 60kHz ∆f 10Hz L 2.35mH µe 48.05 Q 71.8 e 100µV /m
5.6
Amplifier Input Noise
The input noise power (Pn ) and voltage (En ) to an amplifier can be found by: Pn = kT √ o B [12] En = Pn R [13] Where: k = 1.38x10−23 (Boltzman’s constant) To = 290o Kelvin B = bandwidth R = resistance Therefore the noise voltage contribution of the coil DC resistance and the 9.4Ω series “swamping” resistance would be: Pn En B R
3.362x10−18 Watts 5.779nV 840Hz 9.93Ω
The input noise from the coil calculated from this equation is in the ballbark to the nf value obtained in section 5.5 based on the resonant resistance and the total series resistance: Pn En B R
3.362x10−18 Watts 0.477µV 840Hz 67.68KΩ
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References [1] ”Spock: Star Trek: The City On The Edge Of Forever“ [2] “http://www.c-maxgroup.com/products/showProduct.php?id=2“ [3] ”www.digikey.com: P/N 561-1013-1-ND“ [4] ”www.digikey.com: P/N 561-1014-ND“ [5] ”CME6005-A7.pdf“ [6] ”http://www.c-max-time.com/tech/antenna.php Equation in Step 1. NOTE: the original equation from this page is bad.“ [7] ”http://www.amidoncorp.com/aai ferritecores.htm“ [8] ”Andy Przedpelski, A.R.F. Products Inc. I used it about 25 years ago when I worked for him.“ [9] ”Derived from the resonance formula: f =
1 √ “ 2π LC
[10] ”http://www.kongsfjord.no/dl/Antennas/Loop%20Antenna%20Sensitivity.pdf Dallas Lankford. He also cited this equation from: Ferromagnetic Loop Aerials For Kilometric Waves, Wireless Engineer, Feb. 1955, pages 41-46, J.S. Belrose“ [11] ”http://www.kongsfjord.no/dl/Antennas/Loop%20Antenna%20Sensitivity.pdf Equation [10] Solved for n with s/n = 1“ [12] ”Solid State Design For The Radio Amateur: Advanced Receiver Concepts, Page 111“ [13] ”Solving for voltage given the power from equation [12] and resistance.“
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