Passive Electrical Isolation of Double Coil Probes for Localized Spectroscopy and Imaging

Peter Styles MRC Biochemical and Clinical Magnetic Resonance Unit, John Radcliffe Hospital, Headington, Oxford OX2 YDU, UK

A circuit is described for the electrical isolation of double coil probes where separate transmitter and receiver coils are both tuned to the same frequency and are coupled by mutual inductance. There are only passive components in the probe, and so no additional control signals are required for switching between transmit and receive conditions. An analysis of the operation of the circuit is included together with details of component selection and setting-up procedures, thus facilitating the implementation of the design for a variety of applications in both imaging and spectroscopy.

INTRODUCTION

Methods for localized spectroscopy (for review, see Ref. 1) include several techniques where a non- uniform B, transmitter field is used to define position. Some workers have attempted to employ a single surface coil to provide the necessary B, gradient, but it is now generally accepted that more elaborate probe design is necessary for creating a useful B, profile. The design of a suitable probe demands solutions to two problems, namely the choice of a winding geometry to give the required field pattern, and the adoption of a tuning circuit that isolates transmitter and receiver coils. In this laboratory, rotating frame localized

has been applied to the study of a variety of animal and human organs,"' and all these investigations have been done with probes that are designed to satisfy these criteria. In view of the increasing interest in multiple coil probes for both spectroscopy and imaging (for examples, see Refs 4-19), it seems appropriate to provide a comprehen- sive description of the circuits that have been used, including details of component selection and setting- up procedures. The design that will be elucidated may be applied to probes for both spectroscopy and imaging.

ELECTRICAL ISOLATION ~ ~ ~ _ _ _ _ _

The circuits that are used for isolating the two coils from each other are shown in Fig. 1. Brief reports of the two ?arts of the circuit have appeared elsewhere,' but this paper presents a complete description of the principles of operation to facilitate the design and construction of customized probes. One particular feature is that the analysis of the receiver circuit in Ref. 14 has been extended to satisfy the demanding isolation requirements of localization protocols.

The receiver

The receiver protection circuit must be designed to ensure that only a very small current flows in the receiver during the transmitter pluse. Assuming for a moment that crossed diodes X D , behave as a perfect open circuit at low drive voltages (i.e., during the receive period) and a perfect short circuit when driven by the voltage induced during the transmitter pulse, then the receiver circuit may be represented by two equivalent circuits as shown in Fig. 2. Clearly, component values must be chosen such that the circuit resonates during the receive period, but within this restraint there will be an infinite number of possible combinations of tuning capacitor and transmission line. The condition for resonance is

where o = the angular frequency , L , = the receiver coil inductance, C , = the tuning capacitance, 4, = the characteristic impedance of the transmission line and 8 = the angular electrical length of the transmission line. (0 = 2 d / A radians where f = length of line and A = wavelength in the line. The propagation velocity in co-axial cable is dependent on the cable characteristics and this must be taken into account. A typical value of propagation velocity for polyethylene insulated cable is 200m/ps.) Consider next the behaviour of the circuit during the transmitter pulse (diodes conducting). It will be seen that the coil is now terminated by the parallel combination of the tuning capacitor and an inductance (the shorted transmission line). The reactive impedance of these two components is given by

where X , is the reactive impedance presented to the receiver coil during the transmitter pulse. It is

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P. STYLES

RECEIVER TRANS M I T T E R

XSS

Figure 1. The circuit diagram of the double coil probe.

therefore simple to calculate this terminating im- pedance for any combination of transmission line and tuning capacitance which satisfies Eqn (1). Examples are shown plotted in Fig. 3, and four interesting points should be noted. (1) There will always be a maximum permitted length of transmission line (tan 8 = &/wL,), representing the situation where all of the tuning capacitance is provided by the open-circuited line (i.e., C3 is zero). (ii) The form of the X , plot depends on whether the impedance (wLR) of the receiver coil is greater or less than &/2. (iii) When Z, /2 S o L R S Z, then the maximum value of X, will always occur when the transmission line is one-eighth of a wavelength long. (iv) When wL, =s 2,/2 then it is possible to choose a length of transmission line which, in combination with the correct capacitance (C, ) to satisfy the resonance condition (l), will form a parallel tuned circuit during transmit and thus present a very high impedance to the receiver coil.

It is this last condition which needs to be achieved if the receiver coil is to be properly isolated from the transmitter pulse. The condition for resonance of C3 and the transmission line during transmit is given by

Combining the two resonant conditions, Eqns (1) and (3), we arrive at a value for the transmission line

TLI XDI I

Figure 2. Equivalent circuits for the receiver coil and associated components. (a) Those components that are considered in the analysis in the text. (b) The equivalent circuit during the receive period. C,, is the capacitance of the open-circuited line TL,. (c) The equivalent circuit during the transmit period. 4, is the inductance of the shorted line TL,.

length which will give the optimum receiver isolation, namely

z, f (z; - 4 W 2 L 3 ” ’

2 W L , tan 8 = (4)

Of the two possible line lengths, it will normally be prudent to select the shorter.

The transmitter

The isolation requirements for the transmitter coil are less stringent than for the receiver, particularly as this coil is displaced from the sample (see below). Therefore, it is only necessary to detune the transmitter during the receive period. This is achieved by using an additional inductor across the 50 51 input to the transmitter circuit, chosen to resonate with the matching capacitor C6. Thus, in the absence of drive from the transmitter amplifier, C,, and L , form a series tuned circuit which shorts the transmitter coil. As

-1000 1 i I Figure 3. Plots of values of the terminating reactive impedance X, vs the electrical length of the transmission line TL, (reactance is in ohms, and I is the wavelength in the line). Each trace represents a particular value of receiver coil reactance ( o L ) : a, 50 Q; b, 45 9; c, 40 Q; d, 35 52; e, 30 Q; f, 25 Q; g, 20 8. The calculations are for a transmission line TL, with a characteristic impedance (Z,) of 50 Q. Positive values indicate that X, is inductive, negative values indicate that X, is capacitive.

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ELECTRICAL ISOLATION OF DOUBLE COIL PROBES

XD2

Figure 4. Equivalent circuits for the transmitter coil and associated components. (a) The basic circuit. C, is shown dotted because it will typically have a small value, and its function is to 'adjust' the value of L,. (b) The equivalent circuit during the receive period (XD, open circuited). (c) The equivalent circuit during the transmit period.

soon as the transmitter pulse is applied, the series cross diodes XD, conduct, and the output impedance of the amplifier is applied across L, destroying the high Q resonance of C6 and L , . Because of the difficulty in constructing a suitable variable inductor, L I is made rather smaller than required and C7 acts as a means of adjusting its apparent value. L , has little effect on the operation of the circuit during the transmitter pulse because it will typically have an impedance several times greater than 50 &. Equiva- lent circuits for the transmitter coil and associated components are shown in Fig. 4.

Approximations

The above analysis makes certain approximations in the interest of simplicity. The most obvious is that diodes do not behave as perfect open or short circuits. Under conditions of low incident voltage, small signal switching diodes behave as capacitors, typically =2 pF/diode. This can be important during the tuning procedure, but will usually be too small to introduce significant errors in the above calculations. The situation during transmit is more complicated because of the nonlinearity of the diodes. Accurate modelling is very difficult but, as a first approximation, the diodes may be considered as resistors of less than 5 S Z . The principal effect of diodes XD, will be to reduce the Q of the CJtransmission line combination and thus decrease the terminating impedance X,. It is unlikely, however, that this loss of Q will be sufficient to degrade the performance of the probe to any noticeable degree.

A second approximation is that the receiver circuit has been treated as a simple parallel tuned circuit,

with no allowance being made for the matching component. C,. This is reasonable when the receiver coil Q is high, but it should be remembered that the required tuning capacitance C3 will be somewhat less than that given by Eqn (l), and in extreme cases the analysis will need to be adjusted accordingly. C2 is also ignored because the majority of the tuning capacitance should always be placed as close to the coil as possible. If the variable capacitor comprises a significant part of the tuning capacitance then it must be situated at the coil end of the line.

PROBE GEOMETRY

Double concentric surface coil probes have been suggested as being suitable for localized spectroscopy. 1",12~17,18 An improvement on this con- cept involves displacing the transmitter coil so that it is positioned behind a smaller receiver coiL4 All the surface coil localization experiments performed in this laboratory have used probes with a ratio of transmitter to receiver coil radius ~ 2 . 5 . and with the

(a) 2 pos i t ion ( rad ius un i t s )

Y pos i t ion ( rad ius un i ts ) (b) - -3 -2 - I 0 I 2 3

c : c 'I ! : 2 ' n

I

(C) Y posi t ion ( r a d i u s uni ts)

2 L 1

Figure 5. Computer simulation of the signal obtained when using an offset double surface coil probe in conjunction with an eight pulse 'Fourier series window' sequence. The positions of receiver and transmitter coils are indicated by solid circles. The data are presented as contour plots of on resonance signal intensity with contours representing 10% increments of maximum intensity. In (a) and (b) the innermost contour is 100% maximum intensity. In ( c ) the innermost contour is 30% of maximum intensity. (a) and (b) represent the absorption mode signal in two orthogonal planes. (c) represents the dispersion mode signal in the X Y plane. The dispersion mode signals are of opposite sign on the two sides of the probe, and will therefore cancel when the sample is the same in each region. Data kindly provided by Garwood et a/?'

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transmitter coil placed =0.3r, (r, = radius of the transmitter coil) behind the receiver coil. This geometry has three main advantages over co-planar surface coil probes. (1) The receiver coil size and position relative to the transmitter coil result in the contours of equal transmitter flux being substantially parallel to the plane of the coils over the region interrogated by the receiver coil. ( 2 ) Over this sensitive region, the transmitted B, flux decreases approximately linearly with distance from the probe. (3) Regions of very high transmitter flux (close to the transmitter coil) do not occur within the sample, which is of practical significance because many of the localization techniyues have ‘harmonic response’ at places where the B, flux is 3 , 5 , 7 , . . times greater than in the region of interest.

This particular probe design was arrived at more by intuition than calculation. However, subsequent theoretical modelling*’ has confirmed our own experimental findings that regions detected on the basis of equal BI transmitter flux within the sensitive profile of the receiver coil are substantially planar discs, and that the B, variation is approximately linear with distance from the probe. Figure 5, which is taken from the work of Garwood et al. ,,’ shows a simulation of the performance of a probe with the described geometry when used in conjunction with an eight pulse ‘Fourier series window’ sequence.22 This demonstrates the accuracy of spatial localization that is possible with an offset double surface coil design.

The gradient properties of a surface coil transmitter can also be exploited in conjunction with other geometries of receiver coil, as has been demonstrated for animal studies.x.’ The circuits that have been described are suitable for a wide range of geometric configurations.

SELECTING CIRCUIT VALUES

The receiver

It has been pointed out that optimum receiver isolation occurs only when the impedance of the receiver coil (wLR) is less or equal to half the characteristic impedance Z,, of the transmission line. As it will often be convenient to use 5052 co-axial cable for the line, this creates the restraint w L R s 2 5 R . If the measured impedance of the receiver coil is too high, then one of three possible steps should be taken. (1) The coil inductance can be decreased by reducing the number of turns, decreasing its diameter or increasing the wire diameter. ( 2 ) A higher impedance transmission line can be employed (using either standard cable or a custom built transmission line). (3) The effective inductance of the coil can be decreased by inserting in the coil a series capacitance of suitable value C,. (Method (3) is along the lines suggested previously*”*4 for extending the high frequency response of a coil. The resulting impedance will be wLR(,,, = wL, - l/wC,, and the best position for the additonal

capacitor C , is half way round the coil.) When a suitable value for mL has been achieved, the optimum line length can be ascertained from Eqn (4). Application of Eqn (1) will then give an approximate value for the fixed tuning capacitor C3. The fine tune and match capacitors can be placed at either end of the transmission line, but it will usually be most convenient to use the arrangement of Fig. 1. In this case, however, it is important that the variable capacitor C2 be much smaller than Cl, since its effect has been ignored in the preceding calculations.

The transmitter

In order to select the correct inductor for L , , the transmitter coil must first be tuned and matched (using C5 and C6, but without fitting L, or C,) on the most lossy sample that will be encountered. This will determine the maximum value for C, and hence. the minimum value for the ‘black box inductor’ comprising L, and C7. As the effect of increasing C, is to increase the effective inductance of the combina- tion, L, must be chosen such that oL,< ~ / W C ‘ ~ , , , , ~ ~ ) . This may be achieved by temporarily removing Ch from the circuit, and selecting L, so that it will resonate with C6 at a slightly higher frequency than the operating frequency. The subsequent addition of the small variable capacitor C, should then be adequate for fine tuning of the circuit.

TUNING PROCEDURE

The circuits that have been described rely on the nonlinear response of crossed diodes for correct operation. It is therefore imperative that the tuning procedure is carried out under conditions that mimic the operating conditions of transmit and receive. In particular, the receiver circuit must be tuned with the crossed diodes in place (the junction capacitance of the diodes can form a significant part of the resonant circuit), and very low levels of RF, must be employed. Several methods could be used to set up the circuit-the following procedure is one possibility which works well provided that the tuning com- ponents are arranged with only minimal stray reactances in the interconnecting wiring.

(1) Short the transmitter coil and adjust C, and C2 to match the receiver coil to 50 S2. The crossed diodes XD, should be in place. (2) Remove both sets of crossed diodes and replace XD, with a short circuit. Remove the short across the transmitter coil and match the transmitter coil to 50 R using C , and C,. (3) Reconnect the tuning apparatus to the receiver coil. Reconnect both sets of crossed diodes and the cable connecting XD, to the transmitter power amplifier. it should now be possible to bring the receiver back to tune simply by adjusting C,. The circuit is now ready for operation.

The rationale behind this scheme is that, when correctly set up, the combined effect of C6, L, and C, (plus the small effect of the transmitter cable as coupled in via the capacitance of XD,) is to short the

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ELECTRICAL ISOLATION OF DOUBLE COIL PROBES

transmitter coil during the receive period. Therefore, the short circuit applied during (1) above should have an identical effect to the correctly adjusted C,. As mentioned, some thought must be given to the layout of the tuning components and the way in which the short circuit is implemented. Some advice will be given in the next section.

Before using the probe, it is recommended that the transmitter field pattern is checked to ensure that the receiver coil is not making any significant contribution to the flux. A small search coil connected to an oscilloscope will serve as a simple probe to detect the B, field during the transmitter pulse. The observation of a sharp increase in signal occurring very close to the wire of the receiver coil is an indication that the probe is not working correctly.

PRACTICAL CONSIDERATIONS

The measurement of inductance

A simple method for determining inductance involves connecting the inductor to a fixed capacitor of known value, and detecting the resonant frequency of the resulting tuned circuit. The relevant equation is

1 w 2 c '

L=--

where w is the angular frequency of resonance (o = 2nf, f being the frequency in Hz), and L and C are the values of inductance (in henrys) and capacitance (in farads), respectively. The circuit must be constructed using a suitable R F capacitor soldered to the inductor using a minimum of interconnecting leads. The complete assembly can be hung between two small search coils (one connected to an oscilloscope, the other to a frequency source) to ascertain the resonant frequency.2s

Matching to 50 Q

Tuning and matching to 50 S2 may be effected by using an RF bridge of the type described in Ref. 25. Because of the need to make the measurements at low levels of RF, an attenuator must be included between the signal source and the bridge to reduce the excitation to below about 10mV. In order to detect the imbalance signal from the bridge, it will perhaps be necessary to include an amplifier between bridge and detecting device. With a little bit of ingenuity, the spectrometer can be used for this purpose.

Construction of the probe

As the circuits that have been described may find application in a variety of systems and at a variety of frequencies, specific advice is of limited value. However, it is vital that the probe be constructed using good R F practice, and this implies the use of

large surface area materials for interconnection, and a minimum of distance between connected components. The coil L, should be wound so as to have a good Q, and orientated so that it does not couple to the main coils. There are several possible ways of constructing the temporary short circuits and the receiver crossed diodes. One tried method is to incorporate either diodes or a shorting link into BNC plugs, which can then be included into the circuit as appropriate using mating BNC sockets. Although this is not an ideal high Q connection, it works surprisingly well provided that the connectors are maintained in good condition. The crossed diodes should be fast, low capacitance types such as 1N4148. In high power applications it will usually be necessary to increase the current- carrying capacity (particularly for the transmitter set) by parallelling two or more pairs, and perhaps adding further sets in series to reduce the effective capacitance. It must be remembered that most diodes have magnetic leads and, if such types are used, the positioning of these components is important if the probe is to shim.

Shimming

The method that has been used for shimming the magnet is to remove crossed diodes XD1 and use the receiver coil to both transmit and receive the proton signals. The sensitivity to protons may be improved by addition of a further transmission line and tuning capacitors in accordance with the scheme proposed by Gordon and Timms.2h

CONCLUSIONS ~~ ~

The circuits that have been described offer a proven solution to the problem of constructing multiple coil probes where receiver and transmitter must operate independently of each other. Possible applications include surface coil imaging and localized spectroscopy.

In this paper, the emphasis has been on probe design for use with rotating frame localization schemes, and it has been shown that an offset double surface coil probe is theoretically able to generate a B, profile that is suitable for such purposes. In practice, the realization of a working probe is dependent on good electrical isolation. Previously published phan- tom data5 indicate that accurate spatial resolution of planar samples may be achieved using the designs that have been described.

There are, of course, many possible circuits for achieving a similar result. Some of those that have been published use PIN diodes as active switching elements. Such devices could easily be used in the circuits described here, and indeed would perhaps offer improved performance in very high frequency probes, but the need to supply additional control signals to the probe is an extra complication which can be avoided. Another variation is to use lumped circuit elements instead of transmission lines (or vice versa), and in this case the choice is determined by circuit Q

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and ease of construction. Some liberties can often be taken because the Q of the probe may be dominated by eddy current losses in the sample, but it will always be desirable to choose an arrangement which keeps the dissipative components to a minimum. It is this criterion which will largely determine the optimum method for probe isolation. One particular advantage of using a transmission line in the receiver coil is that the receiver tuning components may be placed well away from the active region of the probe. Although co-axial transmission lines can be much more lossy than lumped capacitors, this effect has been mimimized by making the receiver transmission line only a fraction of the total tuning capacitance.

The design rules that have been elucidated have been applied to the construction of a variety of probes ranging from small units for animal work at 32.5 and

73 MHz to much larger coils for human investigation at 32.5MHz. In all cases the calculated component values have given satisfactory performance. However, the realization of a good design depends on an appreciation of the presence of unavoidable stray reactances. Although this problem should only become severe at high frequencies, bad component layout or poor RF practice will inevitably result in a circuit which fails to behave in the predicted manner.

Acknowledgements The author thanks Dr Michael Garwood for helpful discussion and permission to use the data shown in Fig. 5. The Biochemic;il and Clinical Magnetic Resonance Unit i s directed by Professor George K. Radda and supported by the Medical Research Council. the Department of Health and Social Security and the British Heart Foundation.

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Received 29 October 1987; accepted (revised) 20 November 1987

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