WO1996037948A1

WO1996037948A1 - Methods and apparatus for modulating, demodulating and amplifying

Info

Publication number: WO1996037948A1
Application number: PCT/GB1996/001259
Authority: WO
Inventors: Andrew Bateman; Kam Yuen Chan
Original assignee: British Technology Group Limited
Priority date: 1995-05-25
Filing date: 1996-05-28
Publication date: 1996-11-28
Also published as: GB9510679D0; CA2222091A1; EP0835549A1; JPH11505979A

Abstract

The invention includes apparatus for processing an input signal to generate an output signal. The processing arrangement comprises first and second feedback loops for generating, from said input signal, respective output signal components. Each loop comprises a voltage controlled oscillator, having a frequency or phase which is variable in response to a control signal, for generating a loop output signal which forms one of the components of the output signal and a comparator for generating the control signal. There is also provided combining means for combining the loop output signals to derive a signal representative of the output signal. Means for providing first and second feedback loop operating signals, dependent on the output signal and in phase quadrature with one another are provided. In each loop, the feedback loop operating signal is applied to one input of the comparator and the other input of the comparator is coupled to receive a component of the input signal. Signal-stability means for continuously ensuring that the output signal is stable whatever the phase of the output signal relative to the input signal are provided. The signal-stability means and the comparators derive control signals v1 (I) and v2 (II) for the respective VCOs where k = the loop gain of the feedback loops, r = the amplitude of the input signal as represented by the components x and y, R = the amplitude of the output of the VCOs, Δx = the difference between the x component of the input signal and the corresponding Cartesian component of the processed output signal, and (Δy) = the difference between the y component of the input signal and the corresponding Cartesian component of the processed output signal.

Description

METHODS AND APPARATUS FOR MODULATING. DEMODULATING

AND AMPT.TFYTNG The present invention relates to methods and apparatus for processing an input signal (particularly QPSK and ^π/4 QPSK signals), or components thereof, to provide highly efficient linear amplification, modulation and demodulation.

A LINC amplifier has been proposed (see D.C. Cox, "Linear Amplification Using Non-Linear Components", IEEE Transactions on Communications, Vol. COM-22, 1974, pages 1942 to 1945) in which a modulating signal is split into two phase modulated components with constant envelopes which can be amplified separately using highly non-linear but power efficient amplifiers. Combining the two output signals yields the desired linearly amplified signal. With a LINC amplifier the potential for dc to RF conversion efficiency can approach 100%. assuming ideal matching amplifiers. However, in practical LINC amplifiers, the suppression of broadband phase modulation relies on a very tight tolerance on the gain and phase match between the two paths. A gain error of 0.01 dB and a phase error of 0.1 ° give a component suppression of only 54 dB. Such a tolerance is impossible to achieve in a open loop system where much greater gain and phase variations can occur with changes in operating frequency, output power and temperature, and the ageing of components.

International Application No. WO 93/23921 -A, the entire contents of which is incorporated herein by reference, has the same overall objectives as the present invention. The arrangements described in the above application are complicated by stability problems leading to switching complexity from certain phases of input signals. Also some of these circuits suffer to some extent from noise problems when the envelope of an applied input signal such as a QPSK or a ^π/4 QPSK signal goes through zero. The phase locked loops, containing the Voltage Controlled Oscillators (VCOs), of these circuits are stable only when the input signals are in a certain phase range. The switching arrangement attempts to switch the input signal into stable region of operation. The disadvantage of the above arrangements are that the switching is only triggered when the input signal crosses from the stable quadrant into an unstable quadrant. This results in noise being generated when the switching occurs, and the input and output vectors may be out of lock because the VCOs cannot respond with sufficient speed. US Specification 5,105,168 describes a vector locked loop (VLL) which suffers from an input amplitude response which rises with the input signal amplitude. The Voltage Controlled Oscillators (VCO) have an output frequency that is very sensitive to noise and temperature. In the configuration shown in figure 8, in particular, the apparatus may have some initial difficulty in acquiring a lock on the signal because the two VCOs may have output frequencies which are far away from the carrier frequency. Since the two VCO outputs are combined to form the output signal, which is then mixed down and fed back into the input, the feedback signal may be outside the working bandwidth of the circuit. Thus the circuit cannot function properly to pull the VCO back into the working frequency and cannot acquire a lock on the input signal.

According to a first aspect of the present invention there is provided apparatus for processing an input signal to generate an output signal, the processing arrangement comprising first and second feedback loops for generating, from said input signal, respective output signal components and ensuring that the components are correctly in phase for this purpose, each loop comprising a voltage controlled oscillator, having a frequency or phase which is variable in response to a control signal, for generating a loop output signal which forms one of the components of the output signal, or from which one such component is derived, and a comparator for generating the control signal, and combining means for combining the loop output signals to derive a signal representative of the output signal or signals representative of components of the output signal, and means for providing first and second feedback loop operating signals, dependent on the representative signal or representative signals and in phase quadrature with one another, for each loop, applying the feedback loop operating signal to one input of the comparator and another input of the comparator being coupled to receive a component of the input signal characterised in that signal-stability means for continuously ensuring that the output signal is stable whatever the phase of the output signal relative to the input signal.

The VCOs of sensitivity c may receive first and second control signals (vi and vy) according to the equations

where Δφ and Δr are the phase and amplitude differences, respectively, between the input signal to be processed and the processed output signal, r is the amplitude of the input signal to be processed,

R is the amplitude of the respective VCO output signals, and A: is the gain of the feedback loop formed by feeding the processed output signal back to the detectors.

An advantage of the invention is that the system is stable and no switching of the input signals is necessary.

The means for providing feedback loop operating signals may include an oscillator having quadrature output signals, and first and second mixers, one for each loop, for generating the first and second feedback loop operating signals, the mixers both being coupled to receive the said representative signal as one input, and to receive respective quadrature output signals from the oscillator as another input.

The apparatus may also include an amplifier for each loop connected between the voltage controlled oscillator for that loop and a respective input of the combining means.

The input signal may be in the form of Cartesian components x and v and the signal- stability means and the comparators may derive control signals V_] and V2 for the respective VCOs:-

_Vj

where k = the loop gain of the feedback loops, r = the amplitude of the input signal as represented by the components x and y, R = the amplitude of the output signals of the VCOs,

Δx = the difference between the x component of the input signal and the corresponding Cartesian component of the processed output signal, and Δv = the difference between the y component of the input signal and the corresponding Cartesian component of the processed output signal. The above equations are simplified versions of equations which provide the optimum driving signals for the VCOs.

In other embodiments of the invention the phase of a vector representing the input signal is, in effect, changed continuously to always occupy an optimum position for stability. As an alternative, in some embodiments of the invention the input signal vector is so biassed that when the envelope of the input passes through zero, the envelope of the biassed signal does not. Such an arrangement not only reduces noise but also ensures stability.

According to a second aspect of the present invention there is provided apparatus for processing an input signal to provide a processed output signal, comprising a phase detector and an amplitude detector connected to receive an input signal to be processed and a feedback signal as inputs, first and second means for generating first and second component signals having frequencies or phases which are variable in response to first and second control signals, means for combining the first and second component signals in deriving the processed output signal, means for deriving a feedback signal from the processed output signal or components thereof, difference means for deriving the difference between the output signal of the phase detector and a corrected signal derived from the output signal of the amplitude detector to generate the first control signal, summing means for deriving the sum of the correction signal and the output signal of the phase detector to generate the second control signal, and correction means for deriving the correction signal from the input signal to be processed to reduce the dependence of the amplitude response of the apparatus on the amplitude of the input signal.

Methods equivalent to the first and second aspects of the invention and the apparatus claimed also form part of the invention.

In order to avoid the disadvantages outlined above in respect of VCOs, the VCOs may allowed to phase lock onto a voltage controlled crystal oscillator (VCXO). The frequency of the VCXO may be changed by a small fraction by applying a control voltage, and the output frequency is precise and more stable than a normal VCXO.

Embodiments of the invention will now be described by reference to the following drawings, in which:- Figure 1 is a block diagram of a modulator according to the invention,

Figure 2 is a diagram showing vectors relevant to the operation of Figure 1,

Figure 3 is a block diagram of a modulator according to the invention in which control signals according to certain equations are derived from Cartesian components of an input signal, Figure 4 is a simplified version of Figure 3 in which the derivation of the control signals avoids the operation of division,

Figure 5 is a diagram showing the zone which an input vector must occupy for stable operation of the invention,

Figure 6 is a block diagram of a modulator according to the invention in which, in effect, the phase of the input signal is changed to always be optimum for stability,

Figure 7 is a diagram of a modulator according to the invention, in which the input signal is, in effect, biassed from a position where its envelope may go through zero to a position where it cannot do so,

Figure 8 is a diagram of a synthesizer according to the invention employing phase and amplitude detectors and, optionally, means for generating a correction signal, and

Figure 9 is a diagram used in explaining how first order modulators according to the invention may be implemented, and

Figure 10 is a diagram of another synthesizer according to the invention employing phase and amplitude detectors and, optionally, means for generating a correction signal.

Figure 1 shows the basic structure of a modulator employing two feedback loops, each comprising a VCO 10,11, a non-linear radio-frequency amplifier 12,13 and a mixer 14,15, to synthesize an output signal at the output of a summing circuit 16. The input for the circuit is the Cartesian components I and Q, of a signal s(t) separated in a known way or already existing for example in a DSP, and applied as signals x and y to a control signal generator 17. The mixers 14 and 15 receive the output of the circuit 16 and respective quadrature demodulating signals cos ω^/ and sin ω^, where ω_c is the difference in frequency between the signals x and y and the output signals of the VCOs. The output signals of the mixers 14 and 15 are applied to the generator 17.

A vector diagram showing signals relevant to Figure 1 is shown in Figure 2 where the signal s(t) is represented by a vector (18), r, φ, vectors 19 and 20 represent the output signals Rθ _j and RΘ2 of the VCOs 10 and 11 , respectively, and a vector 21 represents the output signal /,α of the summing circuit 16. The vectors 19 and 20 are each separated by an angle θ from the vector 21.

It can be seen that,

θ. + θ, α = — -

2 θ, - θ. θ = 1

Δφ = θ - α

/ = 2R cos θ

where α is the output signal phase from summing circuit 16, φ is the phase of the input signal r,φ, Δφ is the phase difference between the input and output signals and 1 is the output signal amplitude.

It can be shown that in an ideal closed loop configuration of Figure 1 where changes in the input signals x and y are compensated by changes in the output signals of the VCOs 10 and 11, the control signals v_j and V2 applied to these VCOs. respectively are given by

equation 1

equation 2

where c is the sensitivities of the VCOs 10 and 11, r' is — and ω is — . δt δt

In order to realise a practical physical implementation of these equations some simple approximations may be made. For example, it can be assumed that δx/δt is proportional to δx, and δx can be approximated by Δx, which is the difference between the x component of the input signal and the x component of the system output signal. The same approximation can be applied to by/bt, ω and r The control process can then be described by,

V_j =

equation 3 slAR ^ r ²

_Cr JAR ² - r ² equation 4 jfcΔφ kAr v, = equation 5

Y\[AARR

equation 6

where k is the loop gain of the system. From these equations it is possible to devise two generic forms of control circuit implementation - one using Cartesian (IQ) feedback, the other using vector (phase and amplitude) feedback.

Figure 3 shows a modulator which implements equations 4 and 6 and uses Cartesian feedback paths by way of the mixers 14 and 15. The control signal generator 17 comprises a DSP 22 which may either receive the signals x and y or these signals may already be present in the DSP as part of other signal processing. The DSP generates signals al, a2, a3 and a4 where

X π? - y rsjAR ^{2 ■} - r ²

X ? ~ y

X ad - — + y

The signals al, a2, a3 and a4 are applied by way of connections 23 and 25 to a multiplying matrix 24 comprising four multipliers. Two comparators 26 and 27 form Δx and Δy from the signals x and y (sent by way of the DSP 22) and the outputs of the mixers 14 and 15. The output signal amplitude R of the VCOs 10 and 11 is known, and thus the matrix 24 is able to generate the control signals v_j and V2 for the VCOs. The matrix 24 may be constructed from commercially available analogue multipliers when digital-to-analogue converters (not shown) are positioned at the outputs of the DSP 22 or the matrix 24 may be formed by multiplying digital-to-analogue converters at the DSP outputs.

For an input signal phase of φ and an output signal phase of α, the stable locked condition occurs when α equals φ, and all the derivatives of α at α = φ are zero. Using these stability criterion, it can be seen that the modulator of Figure 3 is stable for any input signal phase without the use of the switching arrangements described in the above mentioned application WO 93/23921 -A.

The division process implicit in equations 4 and 6 can be avoided by simplification to the following equations:-

k k v, = - Δx [ -x - y] + - Δy [x - y] equation 7 c c k k v₂ = — Δx [x - y] + — Δy [x + y] equation 8 c c

Equations 7 and 8 can be implemented using the arrangement of Figure 4 where a summing junction 28 and a summing junction 29, arranged to subtract, generate the following signals x + y and x - y for the multiplying matrix 24.

A simplified version can be derived from equations 7 and 8 by hard-limiting the terms (x - y) and (x + y).

k k v. = - - Δx Sgn [x + y) + - Δy Sgn [x - y] c c where Sgn[a] = j ' a ≥ U k k v₂ = — Δx Sgn [x - y] + — Δy Sgn [x + y] c c

After scaling and rotating the system by 45 ^c v, = - - Δx \Sgn [x] + Sgn [-y]) + - Δy \Sgn [ -y] - Sgn [x]) equation 9 c c

v₂ = - - Ax iSgn [~y] - Sgn [x]} + - Δy \Sgn [ -y] + Sgn [x]) equation 10

As is known from the above mentioned application WO 93/23921 -A, the phase locked loops embodying the VCOs are stable only when input signals are in a certain phase range. As a result some two-feedback loop arrangements are only stable when the input vector r,φ is in the semicircular shaded region 31 of Figure 5. The switching arrangements are provided to ensure that the Cartesian components of the input vector are shifted so that this vector is translated to the stable region 31. It can be shown that the optimum phase position of this vector is -45° + 2π«, where n is an integer as shown at 32. In the said above mentioned application, the input signal is restricted by four quadrature switching to one quadrant (the 4th quadrant). From equations 9 and 10 the control signals become:-

v, = -Δy c

The synthesizer of Figure 6 includes summing circuits 34 and 35, and a phase shifter 33 to shift the phases of the input signals for the VCOs 10 and 11 as though the vector r, φ were continuously held in the optimum position shown at 32, as the input vector varies in phase. As a result the output vector 1, α always lags 45° behind the input vector r, φ in the steady state.

The phase shifter 33 ensures that whatever the phase of the input vector, the input signals for the VCOs represent the input vector shifted to the fourth quadrant (bottom right in Figure 5) but the shifted vector tends to settle on either the x or y axis not the position 32. By adding the x and y signals in the summing circuit 34 and subtracting them in the summing circuit 35, the input signals for the comparators 26 and 27 represent an input signal shifted by 45° to the optimum position 32. If the input signal is considered to be re JP, where β is its phase angle, then the phase shifter 33 performs the following complex multiplication

The real part of this equation is the control signal for the VCO 10 and the imaginary part is the control signal for the VCO 11. The denominator normalises the control signals.

Most versions of the modulator of Figure 1, using either Cartesian or Vector feedback, cannot respond fast enough when the envelope of the vector r,φ crosses zero.

The control signal generator cannot respond sufficiently fast to prevent the input and output vectors being out of lock and noise being generated as a consequence. An arrangement which overcomes this problem is shown in Figure 7 where an extra VCO 36 and non-linear amplifier 37 provide an additional input for the summing circuit 16. The output of the amplifier 37 is demodulated using a sin ω_c signal in a mixer 38 with output connected to the inverting input of a comparator 39 which receives they signal at its non-inverting input.

Since the VCO 36 receives the difference between the y signal and its own Q output component after amplification, its output is nearly equal to the Q component of the output signal, plus a time varying portion of the I component. The control signals for the

VCOs 10 and 11 are based on the resultant output signal from the summing circuit 16, and thus the output signals of these VCOs compensate for the output signal of the VCO 36 at that summing circuit. Hence the combined output of the VCOs 10 and 11 is biased to oppose the I component from the VCO 36, which has the effect that when the input signal envelope crosses zero the operating point of the VCO 10 is shifted from zero and so the zero crossing does not affect the control circuit and noise is not generated. Incidentally since most of the Q component is provided by the VCO 36, the VCOs 10 and 11 only provide a small correcting Q component. Since the loops containing the VCOs 10 and 11 function in the normal way the bias, together with any I and Q error at the output is removed at the output as in previous examples. By adding the VCO 39, the inputs to the other VCOs (10 and 11) are mapped to a new position on the vector diagram as follows x - X + _V ^/R ^{2 1} y

Thus the input signal is mapped to the stable region 31 of Figure 5 and no switching or phase shifting (for example in a multiplying matrix) is required.

The operation of the circuit is substantially the same when an optional inverting amplifier 40 with gain equal to 0.5 and an addition circuit 41 are added as shown in dashed lines.

A vector locked loop (VLL) system based on equations 3 and 5 is now described and shown in Figure 8. The phases and amplitudes of an input signal s(t) and a modulated output signal present at the output of a summing circuit 43 are compared in phase and amplitude detector circuits 44 and 45. VCOs 46 and 47 receive input signals from the detectors 44 and 45 by way of a summing circuit 47, arranged to subtract, and a sunrrning circuit 48. Non-linear amplifiers 49 and 50 provide amplified output signals from the VCOs 46 and 47 as input signals to the suniming circuit 43. The output signal of this summing circuit is demodulated using a mixer 51 supplied with a local oscillator signal at a frequency equal to the difference between the output signal frequency of the VCOs 46 and 47 and the frequency of the input signal s(t), and the mixer output is fed back to the detectors 44 and 45.

The signals vj and V2 applied at the inputs to the VCOs 46 and 47 are given by:-

— = θ\ = kΔφ - kΔl c v₂ — = θ"₂ = kΔφ + kΔl c

where Δφ is the phase difference between the input signal phase and output signal phase and Δ/ is the magnitude difference.

The phase response of the feedback loops of Figure 8 is independent of the input signal but the amplitude is a positive function of the input amplitude which increases with input amplitude. To improve performance a correction-signal generator 53 and a multiplying circuit 54 can be added as shown in dashed lines.

The signal generated by the correction-signal generator 53 equals

1 sjAR ² ^ r ² and when used as a multiplier for the Δr signal in the multiplier 54, the VCO input signals conform to equations 3 and 5.

Some other functions which have a positive relationship with the input signal amplitude r can also be used as the correction signal. For example the signal generated by the correction-signal generator may equal

0.045r + -

The correction signal generator may for example comprise a commercially available anti-log circuit or be implemented as part of a DSP program, in a DSP which may form part of an overall system including Figure 8.

The tracking performance of the modulators of Figures 3, 4 and 6 to 9 and other modulators or synthesizers using VCOs or equivalent based on Figure 1, can be improved by adding a loop filter known from VCO theory, at the input to each VCO, thus providing first order modulators or synthesizers. A suitable filter is shown in Figure 9 and comprises an integrator 55, a linear amplifier 56 having a gain of # (a constant value not — dk ) and dt summing circuit 57 adding the usual VCO input applied by way of a path 58 to the output of the amplifier 56. The output of the circuit 57 may be applied as the control signal for each of the VCOs in any of the modulators described, for example one circuit of Figure 9 may be connected between each output of the generator 17 and the respective VCOs 10 and 11 to replace the connections shown in Figure 3. A significant 15 dB improvement in intermodulation suppression has been achieved over a zero order VLL modulator of the type shown in Figure 8 by converting the first order. An alternative to the vector locked loop system of Figure 8 is shown in Figure 10.

In this embodiment the two VCOs, 71 and 72, are synchronised, driven by the amplitude detector 61. In a system where the VCOs function independently, (such as Figure 8) the centre frequencies of the VCOs may drift so far apart as to prevent the system from locking. Therefore the VCOs 71 and 72 may be allowed to phase lock onto a voltage controlled crystal oscillator reference (VCXO 64) using phase locked loops. When functioning, the phase output of the two VCOs 71 and 72 will be the same as the output of the reference VCXO 64. These two phase outputs are combined by the combiner 73 to give the system output. The output signal of this combining circuit is demodulated using a mixer 71 supplied with a local oscillator signal at a frequency equal to the difference between the output signal frequency and the frequency of the input signal s(t), and the mixer output is fed back to the detectors 60 and 61. The output of the amplitude detector 64 is used to drive the VCOs in opposite directions, modifying the relative phase of the two VCO outputs, thus changing the amplitude of the output envelope. The output frequency of the two VCOs 71 and 72 will always be N times the reference signal, where N is the division ratio of the two phase locked loops. The components 75 and 76 which produce this modification of the reference signal may be programmable dividers. It will be realised that the invention can be put into operation in many other ways than those specifically described. For example the VCOs may be any frequency generator having an output signal which can be controlled using a control signal, for example some forms of unstable amplifier or direct digital synthesizers. Other forms of loop filters may be used for first order systems and the control signal generator 17 may be completely or partially implemented in hardware, or computer programs such as a programmed DSP, provided conversion of the DSP output signals to analogue is provided.

As described in the above mentioned application WO 93/23921 -A the modulators described may be reconfigured as demodulators, or as amplifiers without frequency translation, when the multipliers 14 and 15 are omitted, or the modulators may provide frequency translation without the use of a carrier wave.

Claims

1. Apparatus for processing an input signal to generate an output signal, the processing arrangement comprising first and second feedback loops for generating, from said input signal, respective output signal components and ensuring that the components are correctly in phase for this purpose, each loop comprising a voltage controlled oscillator, having a frequency or phase which is variable in response to a control signal, for generating a loop output signal which forms one of the components of the output signal, or from which one such component is derived, and a comparator for generating the control signal, and combining means for combining the loop output signals to derive a signal representative of the output signal or signals representative of components of the output signal, and means for providing first and second feedback loop operating signals, dependent on the representative signal or representative signals and in phase quadrature with one another, for each loop, applying the feedback loop operating signal to one input of the comparator and another input of the comparator being coupled to receive a component of the input signal characterised in that signal-stability means for continuously ensuring that the output signal is stable whatever the phase of the output signal relative to the input signal.

2. Apparatus according to Claim 1 wherein the means for providing the feedback loop operating signals includes an oscillator having quadrature output signals, and first and second mixers, one for each loop, for generating the first and second feedback loop operating signals, the mixers both being coupled to receive the said representative signal as one input, and to receive respective quadrature output signals from the oscillator as another input.

3. Apparatus according to Claim 1 or 2 including an amplifier for each loop connected between the voltage controlled oscillator and a respective input of the combining means.

4. Apparatus according to any preceding claim wherein the input signal has Cartesian components x andy, and, in each loop the signal-stability means and the comparators derive control signals v_j and V2 for the respective VCOs:-

where k = the loop gain of the feedback loops, r = the amplitude of the input signal as represented by the components x and y,

R = the amplitude of the output of the VCOs, Δx = the difference between the x component of the input signal and the corresponding Cartesian component of the processed output signal, and

Δy = the difference between the y component of the input signal and the corresponding Cartesian component of the processed output signal.

5. Apparatus according to Claim 4 wherein the comparators are connected to derive Δx and Δy, and the signal-stability means comprises a signal-processor means connected to receive the components of the input signal and to generate the following signals :-

a2 = ^X ^{cr l} cr^AR ² - r ²

a3 = ^X - ^y cryJAR ² - r ^{2 cr}" a4 ^x _ y

, 2 ^{c *} crxjAR ² - r ² and, multiplier means connected to receive the signals al, al, a3, a4, Δx and Δy and to generate the control signals v\ and V2 therefrom.

6. Apparatus according to any of Claims 1 to 3 wherein the input signal has Cartesian component signals x andy, and the comparators are connected to derive Δx and Δy where

Δx = the difference between the x component of the input signal and the corresponding Cartesian component of the processed output signal, and Δy = the difference between the y component of the input signal and the corresponding Cartesian component of the processed output signal, and the signal-stability means comprises addition means for adding the x and y signals, difference means for deriving the difference between the x andy components of the input signal, and signal processor means connected to receive the outputs of the comparators, the addition means and the difference means, and to derive the control signals for the respective voltage controlled oscillator.

7. Apparatus according to Claim 4 wherein the input signal has Cartesian component signals x and y, and the signal-stability means comprises addition means for adding the x andy signals, difference means for deriving the difference between the x andy signals, and a signal processor means connected to receive the x and components of the input signal and the output signals of the comparators, and to derive the control signals for the voltage controlled oscillators, and wherein the comparators are connected to receive the outputs of the addition means and the difference means as the reference signals.

8. Apparatus according to any of Claims 1 to 3 wherein the signal-stability means comprises means for providing an additional signal for the means for combining the loop output signals which has the effect of so biassing the input signal that when the envelope of the unbiassed signal passes through zero the envelope of the biassed signal as represented by the reference signals, does not.

9. Apparatus according to Claim 8 insofar as dependent on Claim 2 or Claims 2 and 3 wherein the input signal has Cartesian component signals x and y, and the signal-stability means includes an additional loop comprising an additional comparator, additional means for generating a loop output signal having a frequency or phase which is variable in response to a control signal, an additional amplifier connected at the output of the additional means for generating a loop output signal and an additional multiplier for demodulating the amplifier output signal using a signal in phase with one of the quadrature output signals to provide one input to the additional comparator, the other input to the additional comparator being one of the x andy signals.

10. Apparatus according to Claim 9 including means for adding a proportion of the output of one of the comparators but not the additional comparator to the feedback signal applied to the other comparator which is not the additional comparator.

11. Apparatus for processing an input signal to provide a processed output signal, comprising a phase detector and an amplitude detector connected to receive an input signal to be processed and a feedback signal as inputs, first and second means for generating first and second component signals having frequencies or phases which are variable in response to first and second control signals, means for combining the first and second component signals in deriving the output signal, means for deriving a feedback signal from the processed output signal or components thereof, difference means for deriving the difference between the output signal of the phase detector and a corrected signal derived from the output signal of the amplitude detector to generate the first control signal, summing means for deriving the sum of the correction signal and the output signal of the phase detector to generate the second control signal, and correction means for deriving the correction signal from the input signal to be processed to reduce the dependence of the amplitude response of the apparatus on the amplitude of the input signal.

12. Apparatus according to Claim 11 including mixer mean for frequency translating the processed output signal or components thereof in providing the feedback signal by an amount equal to the difference in frequency between the outputs of the said first and second means, and the input signal to be processed.

13. Apparatus according to Claim 11 or 12 wherein the first and second means are VCOs of sensitivity c and receive first and second control signals (v_j and V2) according to the equations

where Δφ and Δr are the phase and amplitude differences, respectively, between the input signal to be processed and the processed output signal, r is the amplitude of the input signal to be processed, R is the amplitude of the respective VCO output signals, and k is the gain of the feedback loop formed by feeding the processed output signal back to the detectors.

14. Apparatus according to Claim 11 or 12 wherein the first and second means are VCOs of sensitivity c and receive first and second control signals (v_j and V2) according to the equations fcΔφ kAr _{/Λ Λ yI C} R . v, = — (0.045r + — ) c c 2

fcΔφ kΔr ,_{Λ Λ Λ} R . v, = — + (0.045r + — ) c c 2 where Δφ and Δr are the phase and amplitude differences, respectively, between the input signal to be processed and the processed output signal, r is the amplitude of the input signal to be processed, R is the amplitude of the respective VCO output signals, and k is the gain of the feedback loop formed by feeding the processed output signal back to the detectors.

15. Apparatus according to any preceding claim including a respective integration and addition circuit for and with output connected to the input of each means for generating a loop output signal, for adding the integral of the input signal for that means to that input signal.

16. A method of processing a input signal to generate an output signal including the steps of using first and second feedback loops to generate, from said input signal, respective output signal components and ensuring that the components are correctly in phase for this purpose, for each loop, generating from a voltage controlled oscillator, having a frequency or phase which is variable in response to a control signal, a loop output signal which forms one of the components of the output signal, or from which one such component is derived, combining the loop output signals and the input signal to derive a signal representative of the output signal or signals representative of components of the output signal, generating feedback loop operating signals, in phase quadrature with one another, from the representative signal or representative signals, one for each loop, and for at least one loop, comparing the feedback loop operating signal with a component of the input signal to provide the respective control signal ensuring that the output signal is stable whatever the phase of the output signal relative to the input signal.

17. A method of processing an input signal to provide a processed output signal, comprising generating first and second component signals having frequencies or phases which are variable in response to first and second control signals, combining the first and second component signals to derive the output signal, deriving a feedback signal from the processed output signal or components thereof, deriving the difference between the output signal of the phase detector and a corrected signal derived from the output signal of the amplitude detector to generate the first control signal, summing the correction signal and the output signal of the phase detector to generate the second control signal, and deriving the correction signal from the input signal to be processed to reduce the dependence of the amplitude response of the apparatus on the amplitude of the input signal.