FREQUENCY
4. IMPEDANCE MATCHING OF COILS
4.1 Matching Devices
4. ENDORCOILS AND RELATED RADIOFREQUENCY CIRCUITS 187
Table8. Network parameters ofa stripline coil 1116" x I".
f(MHz) R(O) X(O) LorC SWR (1 : )
0.15 49 .8 4.3 4.5 IlH 1.09
0.25 50.1 2.8 1.8IlH 1.06
0.50 50.3 2.3 0.75 IlH 1.05
1.00 50.5 3.0 0.47 IlH 1.06
1.50 50.9 3.9 0.41 IlH 1.08
2.00 51.4 4.8 0.38 IlH 1.10
2.50 52.1 5.8 0.37 IlH 1.13
3.00 52.7 6.7 0.35 IlH 1.15
3.50 53.6 7.6 0.341lH 1.18
4.00 54.5 8.4 0.33 IlH 1.20
4.50 55.5 9.2 0.33 IlH 1.23
5.00 56.7 9.9 0.32 IlH 1.25
5.50 58.0 10.5 0.31 IlH 1.28
6.00 59.4 11.1 0.291lH 1.30
6.50 60.9 11.5 0.281lH 1.33
7.00 62.3 11.8 0.271lH 1.36
7.50 64.4 12.0 0.25 IlH 1.39
8.00 65.4 11.9 0.241lH 1.42
8.50 68.4 11.7 0.221lH 1.45
9.00 70.5 11.2 0.20 IlH 1.48
9.50 72.7 10.5 0.18 IlH 1.51
10.00 74.9 9.5 0.15 gH 1.54
moment require higher radiofrequency power so that the radiation-induced spin transitions are temporally competitive with spin relaxation. Under these latter conditions power losses due to the ENDOR coil mismatch may be unacceptable, and one must introduce a matching device in the form of a reactive element or transformer so that the coil has an effective impedance of 500.
The data compiled in Section 3 show that each coil undergoes a variation of its impedance as the carrier frequency is swept, and therefore no characteristic impedance exists for a given ENDOR coil. At best, one can match a coil to 50 0 at some prescribed frequency within the sweep range , usually the center, and allow for small deviations of the impedance at frequencies above and below the point at which the coil is matched. The slope of the impedance deviation will be proportional to the coil's inductance, and one may either sweep over a frequency range that is determined by the acceptable fluctuation of power (e.g. ± 1.5 dB) or use a low-inductance coil so that the slope of the deviation is smaller. For example, the 120 helix is matched to 500 at 15 MHz, and sweeps ranging from 5-25 MHz are acceptable since the power fluctuation across the sweep range is less than 3 dB, which is the power deviation used to define the pass band of a filter. A different sweep range might be used at another center frequency (e.g.45 MHz) where the slope~/l:i.f is different.
One may use broadband transformers or modified networks as a means to match an ENDOR coil. Transformers are the most convenient and intuitive means of matching because they are easily inserted into the transmission line circuit, and their design can be understood in terms of a turns ratio that inter-relates the coil impedance Z and the line to be matched Z o. In the case of the 20tum helix, the impedance at 15 MHz is matched with a 1:4 transformer; at 5 MHz, where the impedance is approximately 25 0 , one would use a 1:2 transformer,etc.
A very simple transformer that may be understood in terms of a turns ratio is illustrated in Figure 13 and may be found in many handbooks on radio engineering. Two brass tubes (-1.4" dia.) are soldered onto a copper plated square of circuit board (two holes drilled to accept the tubes), yielding a horseshoe shaped conductor. Ferrite toroids are stacked on each brass tube, and a second circuit board square is soldered onto the other end of the brass tubes. Unlike the first square , however, the copper plate is etched away between the two solder points so that there is no closed loop of conductor material. Wire is then looped through the brass tubes as many times is necessary in order to provide the desired turns ratio.
An alternative form of transformer that is somewhat less intuitive with respect to the turns ratio has been described by Ruthroff (1959) and Guanella (1944). The advantage of these transformer types , as opposed to the transformer that was described in the preceding paragraph , is that they are
4. ENDORCOILS AND RELATED RAoIOFREQUENCY CIRCUITS 189 very easily rendered compatible with standard transmission lines in a drop-in configuration. These transformers operate on the principle of summing
FERRITES STACKED OVER BRASS TUBE
/
---
FOUR TURNSOF COPPER WIRETOP VIEW
COtIOUCTOR MAnllW.
ETCHED AWAY
PRINTEDCIRCUITBOARO
HOLE TO ACCEpT BRASS TUBE
END VIEW 1
•
END VIEW2Figure /3. An impedance matching transformer that is based upon a turns ration of conductor loops . A single loop is fashioned from a pair of brass tubes through which are passed several turns of copper wire .
voltage with a delayed voltage at specific terminals, and depending on how one sums the voltages (usually via tapping or multiple stages), one can control the turns ratio (Ruthroff, 1959; Guanella, 1944; Sevick, 1990). .
Radio engineers use transformers to match antennas to transmitters, and the transformers of Guanella and Ruthroff are designated according to the symmetry of the antenna. A balanced circuit element is symmetric with respect to a feed point, whereas an unbalanced element is defined as one that is not symmetric with respect to a feed point. For example, a section of coaxial line is unbalanced because the signal radiates down the center conductor only. This is in contrast to dipole antenna, which is balanced because both arms radiate. It therefore follows that the ENDOR coil is an unbalanced device and the type of transformer one wishes to use is the unbalanced-to-unbalanced, or unun, transformer. In a given circuit, the transformer can be imagined as simultaneously being a load to the source and a source to a low impedance load; the ENDOR circuit requires a pair of transformers to separately match the coil/cavity to the power amplifier and the 50
n
termination. It is also important to recognize that these transmission line transformers operate via reactive coupling and therefore behave as a bandpass filter that should feature a flat response over the desired frequency range.2 4
3 LEAOS2&3 SOlOEREDTOGETHER
Figure 14. Transmission line transformers of the Ruthroff (top, left) and Guanella (bottom, left) type. Construction details for the Ruthrofftransformer are illustrated on the right.
A schematic diagram of both Guanella and Ruthroff 1:4 unun transmission line transformers is illustrated in Figure 14. The devices are constructedbywrapping a section of a conductor pair around a ferrite rod or toroid, and then attaching the exposed leads to the remainder of the circuit as indicated. The wire pair can be fabricated by taping together two segments of enameled magnet wire (side-by-side); alternatively, one may obtain a specialized two-conductor wire (MWS Wire Industries, Westlake Village, CA) or a narrow coaxial cable as the conductor pair. The wire pair may then be tightly wound, twisted, or simply paired. The principal design considerations when constructing a transformer are the matching ratio, the power handling capability, and the characteristic impedance (of the transformer itself). Ruthroff (1959) demonstrated that the optimal performance of a transformer is obtained when its characteristic impedance is the geometric mean of the operating input and output impedances, plus or minus 10-20% (e.g. 25
n
for the 50:12 matching transformer). The characteristic impedance is adjusted by trial and error and based upon experimental trends that follow from the physical dimensions of the wire, the ferrite core, etc. (Demaw, 1980; Sevick, 1990).The power handling capability of the transformer depends upon the size (diameter and cross-sectional area) of the ferrite and its permeability, both of which determine ability of the coil to dissipate heat. Sevick (1990) reports data that are compiled from many trial and error studies, and, in general, the trends show that lower permeability (less than 300) ferrites better handle high power. Low permeability coils, however, require more turns. According to Sevick (1990), a 1 inch diameter ferrite of permeability less than 300 is adequate for handling power up to 200 W; a 1 kW transformer requires a toroid with a minimum diameter of 1.5 inches . The power handling capability of a transformer is tested by the so-called 'soak test', which entails
4. ENDORCOILS AND RELATED RADIOFREQUENCY CIRCUITS 191
the application of 1 kW radiofrequency power for a period of time and determining whether the transformer coil becomes overheated.
iii W
s
14.0 dB :it11.0 dB
en (,)
e en
0 e
~ 0
0 ~
w 0
t: ~
~en :iE
~
UJZ... ~
It~ Itw
0n,
~
c,50 150 250 350 450 30 40 50 60 70
FREqUENCY (MHz) FREQUENCY (MHz)
Figure 15. Power transmission plots (log P) for a 20-tum copper helix without (left) and with (right) a 1:4 Ruthroff impedance matching transformer. Since the transformers themselves have only a limited operating bandwidth, the optimum range only is illustrated. Note that the power transmission plot is much flatter in the 25-70 MHz range.
The optimum frequency range of operation can be controlled by altering the characteristic impedance of the transformer with, for example, low-impedance windings. DeMaw (1980) describes transmission line transformers that are optimized for low frequency operation and wound with 25
n
coax instead of 14-18 gauge wire; stripline also works well (Sevick, 1990). Improved high frequency performance is obtained with a trifilar version of the Ruthroff transformer (Sevick, 1990). Twisting the wire pair apparently has little effect on the performance of large toroidal (<<Po ~ 1 in.) transformers. The rationale behind twisting the wire is that one obtains improved coupling between the lines, but the benefits of this technique seem to be significant only for very thin wire (Sevick, 1990).Practical impedance matching transformers that have been used for cw-ENDOR were constructed on the Ruthroff design by using 4-5 turns of a twisted pair of 14 gauge wire. Toroids of 0.7" diameter and low permeability (Micrometals, Anaheim CA) work well below 70 MHz and at powers as high as 200 W. Figure 15 illustrates the modified transmission profile of a 20 tum helical ENDOR coil after being matched by a 1:4 Ruthroff transformer.
The noteworthy aspect of this network analysis is the flattening of the response, bearing in mind that the ideal 'match'(i.e. 1:4, etc.) applies at only one frequency in the sweep range. In other words, if one had a purely resistive load of 12.5
n,
then one would observe a fairly flat response over a bandwidth that is determined by the transformer. One the other hand, if theload is reactive, then the transformer is not going to compensate for changes in Z, and the power will still fluctuate as the frequency is swept.