GB2253532A - A resonator - Google Patents

Abstract

This invention relates to resonators, particularly for use in narrow band high frequency filters, e.g. in the 900MHz region. A track of circuit board (20) of relatively low inductance is coupled in series with a resonator (11, 12) of relatively high inductance. The track of circuit board (20) is of a calculated length such that the tapping of this track by an input (10) or an output (13) provides a means of supplying a specified impedance for an arm of a circuit containing the resonator and the track. Resonators (11, 12) may be disposed in separate enclosures or shields and inductively coupled via apertures on the shields to form a resonant transformer. The track (20) may be formed by micro-strip lines, transmission lines or spiral conductors. <IMAGE>

Description

A Resonator.

Background to the Invention.

This invention relates to the tapping of resonators and particularly to the tapping of helical resonators within narrow band radio frequency filters.

Summary of the Prior Art.

Conventional filters are a standard component incorporated within electrical circuits. These filters are electrical networks which transmit or suppress signals within certain designated frequency bands. Indeed, there are in fact four distinct varieties of filter which attenuate the signal between various cut-off points. An example of one distinct type of filter is the Butterworth filter. The Butterworth filter operates in a region referred to as the pass-band.

Filters are constructed from either active or passive components. Active filters are characterised in that they contain, for example, operational amplifiers which introduce gain into the signal through a suitable R-C feedback loop to produce the desired frequency response while most passive filters rely upon impedances arranged in shunt and/or parallel configurations (L-C networks) in order to achieve this same effect.

A conventional method of producing the inductance, L, of a filter is to use a helical coil. The helical coil serves as a resonator. One such configuration is the coupled resonator filter wherein two or more resonant circuits are coupled to: (i) each other, (ii) a source and (iii) a load.

The helical filter of Figure 1 utilizes helical resonators coupled to each other by apertures in the resonator shields (not shown). Prior art teaches that these helical filters are tapped somewhere along their length in order to acquire the correct impedance for that arm of the network. However, problems arise when one attempts to tap a resonator designed to operate at high frequency and within the confines of a narrow frequency band. In such cases, it is necessary to tap the resonator at precise locations around the helical resonator. The degree of precision required in tapping narrow band high frequency filters is, typically, within less than one quarter of a turn of the helix. This is extremely difficult to achieve and, additionally, is difficult to reproduce.Furthermore, space limitations which arise in printed circuit boards also hinder the ability to accurately tap a helical coil.

It can therefore be appreciated that there is a requirement within the art to provide a means of tapping a resonator wherein an accurate, precise, reproducible impedance is obtained for a specific network of components within a circuit. The application of such an invention would be particularly applicable to the area of narrow-band high frequency filter circuits.

Summary of the Invention.

This invention addresses at least some of the disadvantages which arise in the described prior art. A resonator of relatively high inductance is coupled directly in series with a track of circuit board having a relatively low inductance. This track of circuit board is of a calculated length such that tapping of this track provides a means of supplying a specified impedance for an arm of a circuit containing the resonator and the track.

The advantages gained from such a method and configuration of tapping a helical resonator are numerous.

The tapping of the track of circuit board provides a technique of manufacturing narrower high frequency filters.

In addition to this benefit, tapping of the track eliminates the necessity of having to tap the resonator directly.

Consequentially, a simplification of both the circuit and the construction thereof is achieved. The tapping of the track also provides an increased ability in being able to control the impedance transformation ratio of a circuit.

Finally, since the track is tapped to obtain a specified impedance for an arm of a circuit containing a resonator and the track, the construction parameters for the resonator are not as critical as before and a wider range of existing resonators can therefore be used. In precis, the invention provides a simplified, reproducible method of supplying an accurate, specified impedance for an arm of a circuit while still retaining the full advantages of a helical resonator.

A preferred embodiment of the invention will now be described by way of example only, with reference to the accompanying drawings.

Brief Description of the Drawings.

Figure 1 illustrates a prior art resonant transformer comprising two tapped helical filters.

Figure 2 illustrates, in accordance with a first preferred embodiment of the invention, a resonant transformer comprising two helical resonators which are both in series with tapped low inductance coupling lines.

Figures 3 & 4 illustrate two alternative embodiments of a resonant transformer employing the tapping of at least one of the resonators in accordance with a second and third preferred embodiment of the invention.

Figure 5 illustrates the application of the invention in tapping a resonator which has been incorporated within an oscillator.

Detailed Description of the Preferred Embodiment.

Figure 1, refers to a prior art resonant transformer containing a primary helical resonator (11) and a secondary helical resonator (12). The primary (11) and secondary (12) resonators are respectively coupled to an input (10) and an output (13) of the transformer by means of tap coupling. The bottoms of the resonators (11, 12) are both connected to ground potential whereas the tops of the resonators remain in an open-circuit configuration. Thus, in the case of narrow band filters, a step up impedance transformer is produced Figure 2, refers to a transformer (similar to that of Figure 1) which incorporates micro-strip lines (20) directly in series with both the primary and secondary resonator windings (11, 12). These micro-strip lines (20) are printed on a circuit board and have an inductance which is relatively low compared with that of the resonators (11, 12).A first micro-strip line, which is connected in series with the primary resonator (11), is tapped by an input (10). A second micro-strip line, which is connected in series with the secondary resonator (12), is tapped by an output (13).

The ends of the two micro-strip lines (20) are both connected to ground potential. As in the described prior art, the tops of the resonators (11, 12) remain open-circuit. It should be noted that the micro-strip lines could be replaced by alternative forms of inductive coupling lines e.g.

transmission lines or spiral inductors.

The inductance of each micro-strip line (20) is calculated such that the series combination of this inductance together with the larger inductance of the helical resonator (11, 12) produces the desired resonator impedance loading. The following mathematical calculation will demonstrate the improvement which is experienced through the utilisation of the invention over the convention method of resonator tapping.

By way of example, the production of a Butterworth Filter having a central frequency, fO, of 900MHz (1MHz = 1 million cycles per second) and a bandwidth, BW, of 18MHz (i.e. 2%) is now undertaken. For purposes of the example, source and load impedances will be set at a value of 50Q. Numerical calculations are based upon a helical resonator having a square cross-section of 0.3 inches.

Referring to pages 500-501 of A. Zverev's "Handbook of Filter Design", it can be seen that the number of turns per inch in a resonator coil, n, (of rectangular cross-section) can be expressed by the equation:

where b, d & d are dimensional parameters of the helical resonator and fc is the central frequency expressed in MHz.

The total number of turns N is therefore given by

turns (2) The characteristic impedance Z0 of the resonator is expressed by the equation

With a resonator of rectangular cross-section and with ratios for the lengths of the sides and the hypotenuse being: d = 0.55 and b = 1.5 (4) D d equation (3), the characteristic impedance Zo, reduces to

Furthermore, if the resonator shield is of square crosssection with the length of a side S = b = d = D/1.2, then equations (1), (2) and (5) simplify to

respectively. Equation (7) stipulates that the desired (example) resonator requires 5.9 turns of a 0.3 inch square coil. However, in practice, only 5 turns of the helical coil are required for the production of a 900MHz filter.

This is the result of tuning core loading and would therefore be apparent to one skilled in the art.

The Quality Factor, Q, of the resonator is defined by the equation

As can be seen from equation (9) above, the denominator effects the Q-factor. Losses due to the power dissipated are predominantly the result of losses in the conductor, shield and, to a lesser extent, the dielectric. However, there are also additional losses owing to currents in the shield.

These additional losses result from the resistance of the coil, Rc, and the resistance of the shield, Rs. If P0 and P5 are assumed in series and by ignoring the negligible dielectric losses, the unloaded Q-factor of the resonant line is expressed as

For a resonator with a copper coil and shield, equation (10) can be expressed in terms of the dimensional parameters of the resonator. Therefore the unloaded Q-factor is found to be

The simplified equation (12) is accurate to +/- 10% and is based upon limitations imposed by the ratios of the resonator dimensions and the skin depth. From equation (12) the unloaded Q-factor for the desired resonator in the example is calculated to be Qu = 540 (13).

Observing the resonator from the bottom of the winding and applying circuit analysis, it is discovered that a quarter wavelength open transmission line is present. The equivalent parameters for the L, C and R components of this transmission line are

#Z0 R - = 0.4fl (16) 4Qu where fg is in hertz. These equations are derived from the mathematical manipulation of the expressions of a resonant transmission line with low losses.

Referring to pages 295-310 and page 341 of A. Zverev's handbook "Predistorted Parameter Design of Coupled Resonator Filters", the Butterworth Filter in the example requires a loaded Q-factor of

Therefore the series resistance to the resonator is

Consequentially, the resistance which must be reflected from the 50Q load impedance in series with the resonator must be Rp = (4.0 - 0.4)so = 3.6Q (19) It should be apparent that the inductance of the micro-strip line (20) must now be calculated to present such a series resistance to the resonator. The micro-strip line (20) at the input to the resonator can be modelled on a parallel combination of a small inductance and a 50Q resistance.

Equivalent RF circuit transformation of this inductance and resistance generates the approximation

where rs is the series equivalent resistance; Rp is the resistance of the micro-strip line in a parallel configuration; and Ql is the Q-factor of the loaded micro-strip line.

This approximation is valid at RF frequencies and for Qfactors which satisfy Q2 > 10.

Rearranging equation (19) gives

The value of this parallel Q-factor is sufficient to justify this transformation. The required inductance of the microstrip line (20) is obtained by equating equations (18) and (20) and rearranging in terms of L. Thus,

An inductance of this size will have a corresponding reactance, X, equal to X = OL - #C where ois the angular frequency. However, in this case, C=0. Therefore X = 2xfoL = 14# (23) and the Phase Angle # is given by tan =R R (24) A 77Q line of electrical length 10 would provide the required reactance. This could, for example, be obtained by using a track of length 5.08mm and width 1.27mm located on a G-10 substrate.

The application of this invention is suitable for tracks of circuit board having a calculated inductance value of 10% or less of the inductance value of the helical resonator/coil. Track inductance values between lnH and 15nH would be realised by micro-strip lines whereas inductances greater than 15nH would, typically, employ spiral inductors. A lnH inductance would require a micro-strip line 2.16mm in length. The reproducibility of such minute strips present, at present, the lower limiting factor of the track inductance.

If a Butterworth Filter were constructed the conventional way (i.e. using a tapped resonator), the following equations and calculations would be valid. Once again with reference to Zverev's "Handbook of Filter Design" pages 506-508, the doubly loaded Q-factor, Qd for the circuit is

where qi is the normalised quality factor = 1.414 (obtained from tables of 3-dB down k and q values).

By applying transmission line theory, the following equation is applicable:

where Rb is the equivalent load resistance.

In addition, transmission line theory also provides an expression for the electrical angle 0.

and solving for 0 0 = 2.10 The location of the conventional tap from the grounded end of the helical resonator is then found at N(tap) = (90) N (Resonator) = N (Resonator) (28) Typically, a 900MHz resonator consists of 5 turns of a helix.

In such a case, the location of a tap for a 900MHz Butterworth Filter having a bandwidth of 18MHz would be 42/360 (0.12) revolutions around the fifth coil. Clearly, such accurate tapping of a resonator is not easily reproducible and would be extremely difficult to achieve.

The invention would be equally suitable for resonators with between 1 and 50 coils.

Flux coupling between adjacent micro-strip lines of the primary (11) and secondary (12) resonators is avoided by ensuring that the the micro-strip lines are separated by a sufficient distance (-lcentimetre). It should be apparent to one skilled in the art that alternative methods of restricting flux coupling between these two micro-strip lines could also be employed e.g. the use of shielded transmission lines.

It will be appreciated by one skilled in the art that Figures 3 S 4 are alternative embodiments of the invention (as previously disclosed) which requires only one micro-strip line (20) in order to produce the required impedance for a circuit. These configurations would arise in the event that either the primary (11) or secondary (12) resonators were initially tapped or constructed with the correct inductance.

Figure 5 illustrates an application of the invention in the field of oscillators. A helical resonator (11) is coupled in series with a micro-strip line (20) which is in turn coupled in series to a resistance or load (50). The other end of the load (50) is connected to ground potential.

An input (10) is coupled to the open end of the resonator (11). An output (13) is tapped from the micro-strip line.

The micro-strip line (20) is loaded by the reflected external load (50). Thus, the micro-strip line has the effect of preventing the reflected load (50) from appearing across the resonator (11). The result of the isolation of the load (50) is that the quality factor, Q, of the resonator remains high.

It can, therefore, be appreciated that an invention so designed and described would produce the novel advantage of an improvement in the ability to reproduce accurately narrowband high frequency filters. Furthermore, the invention permits the accurate construction of higher definition narrow band filters in as much as narrower pass-band regions can now be defined. Additionally, the process of tapping resonators has been simplified. A further benefit arises from the ability to utilise an increased number of "off the shelf" resonators. This is a result of being able to adjust the impedance of the circuit by appropriately calculating the length of the micro-strip line and/or the position of the tap thereon.

It will, of course, be understood that the above description has been given by way of example only, and that modifications of detail can be made within the scope of the invention.

Claims (9)

Claims

1. A resonator of relatively high inductance coupled directly in series with a track of circuit board having a relatively low inductance wherein the track is tapped in order to provide a specified impedance for an arm of a circuit containing the resonator and the track.

2. A resonator as claimed in claim 1, wherein the inductance of the track of circuit board is 10% or less of the inductance of the resonator.

3. A resonator as claimed in claim 2, wherein the inductance of the track lies in the approximate range of lnH to 15nH.

4. A filter comprising a first resonator and track as claimed in claim 1,2 or 3 and a further resonator, forming a transformer arrangement therewith.

5. A filter as claimed in claim 4, wherein the further resonator comprises a resonator of relatively high inductance coupled directly in series with a track of circuit board having a relatively low inductance and a tap associated with the track.

6. A filter as claimed in claim 5, wherein the ends of the tracks remote from the resonators are connected to a common source of potential, and wherein the tap of the first resonator provides an input to the filter and the tap of the further resonator provides an output from the filter.

7. A filter as claimed in claim 4, wherein the further resonator is a tapped helical coil.

8. Radio communication circuitry comprising: (a) a signal source; and (b) a filter of any one of the preceding claims 2 to 7, wherein the source is connected to a tap of one of the resonators and a filtered signal is derived from a tap of the other of the resonators.

9. A method of obtaining a specified impedance for an arm of a circuit by tapping a track of circuit board in series with a resonator.