DE1285577B - Procedure for phase difference measurement - Google Patents

Description

position of a moving object, for example a satellite, can be "determined" by the phase difference of the signals received in the receivers 24 and 25 of the satellite transmitter, which emits signals of a frequency F ₀ , for example 1.5 GHz, whose phase as Reference phase is assumed to be zero. It should also be noted that the received signals are subject to the Doppler effect.

carried out, the Doppler shift can be considered constant during the time of a single measurement to be viewed and neglected. The signal picked up by the receiver 24 has

a frequency F ₁ = F ₀ + AF ₁ (MHz), where, -1F ₁ = ^ Spund U _{1 represents} the corresponding phase shift measured in radians, based on the frequency

for phase difference measurement, in which this phase difference can be determined directly.
It is also an object of the invention that the

From the article by JT M e η ge 1 in Proc.
IRE, June 1956, pp. 755 to 760, entitled "Tracking the Earth Satellite, an Data Transmission, by
Radio «it is known that the phase difference of a
radio frequency signal transmitted by a satellite and received in two remote tracking stations, proportional to the intensity of the received signals; However, if the phase-direction cosine in the tracking stations is satellites in sufficiently short time intervals to measure the difference. Thus the value of the direction cosine
is known at all times of the satellite's flight over the tracking stations, the phase difference measurements must be carried out at a high repetition frequency 15
be performed. If a computer is used to measure the phase difference, the
two measured phase values to be subtracted
first digitized, and only then is the subtraction

executed. As a result, in each of the digitized 20 sequence F ₀ with the phase angle zero; that introduced a certain error by the Emp values, so that the signal picked up by the receiver 25 has a frequency result also has a considerable error. _P _ _{F. F} , _UH7l , " _η κ _Ρ1 · if _" 2 " _n A" ₍ y. _P

τ - »- τ- 1-1 ι · j 1 1 χ ·· 1, 1 · 1 ι 1 - i JT7 ⁼⁼ Fn -T -1 Γι I1V1JHZ), WOucl AFn - - ^ - and (l-> die

However, this error can be considerably reduced by 20 ζ - 2π

if the phase difference is determined first and the corresponding phase shift in radians of this value is then digitized. 25 represents measure, based on the frequency F ₀ with

It is therefore the object of the invention to provide a method for zero phase angle. Are in every moment

the values H ₁ and a ₂ for the phase shift and thus the values for the frequency shift 1 F ₁ and AF ₂ generally differ from one another,

Measurement method under difficult noise conditions 30 because in general the distances from able to work. Satellites to receivers 24 and 25 different

The main feature of the invention is that the
Phase difference measurement method a first control loop
in the manner of a so-called frequency negative feedback
contains the input of which the first input signal to 35
and whose output signal is formed
by the voltage of a first controlled oscillator that is included in the control loop that
a second control loop of the same type is also provided
whose input the second input signal has one 40 Hertz. is given and the output signal is formed The input signal of the frequency F ₁ or that of the

by the voltage of a second controlled oscillator frequency F ₀ with the phase angle U ₁ is from tors, which is contained in the control loop; an antenna 1 (receiver 24, Fig. I) is recorded the voltage at the output of the first controlled men and in an amplifier 3 with the amplifier oscillator in the negative feedback path of the second 45 gain factor G ₁ with low self-noise E ₁ so the control loop is introduced a second output amplified that no phase shift is introduced with a signal corresponding to the phase difference. The output signal of the amplifier 3 is phase, that is the output signal of the second input of a control loop, the Zv / corner of which it is, controlled oscillator generated. to generate an intermediate-frequency output signal,

The invention is illustrated in more detail with reference to Figures 50 its phase and frequency with the phase and the explained, of which the frequency of the input signal are firmly linked.

F i g. 1 an embodiment of the invention- The control loop also contains a mixer 4, according to the phase measurement method in the block diagram of an intermediate frequency amplifier 5, one phase; comparator 6, a low-pass filter 7, a controlled one

F i g. 2 shows the servo loop of a receiver 55 oscillator 8, which has a center frequency of 13 MHz the F i g. 1; oscillates, and another mixer stage 9. On terminals

Fig. 3 shows the servo loop of the other receiver 10 and 11 are the voltages of a normal catcher; in . frequency generator (not shown), whose Aus-F ig. 4 shows a receiver which has an output frequency of 30 MHz or (F ₀ + 17) MHz, both part of the apparatus for the phase measurement method 60 with the phase angles zero; forms these signals. are connected to the phase comparator via a 90 ° element

The apparatus 6 or mixer 9 required for the phase measurement process is entered. rature of the F i g. 1 contains two receivers 24 and 25, the input signal of frequency F ₂ and that of the

which are installed in two distant (distance at frequency F ₀ with the phase angle a ₂ is for example 10 km) receiving stations. 65 of an antenna 2 (receiver 25) and the two receivers are connected to one another by means of a radio link with 26 being in an amplifier 13, which has a high gain. factor with low intrinsic noise, without introducing means of such an arrangement, the angulation of a further phase shift can be increased.

are. It should be noted that due to the Doppler effect, the frequency shifts / IF ₁ and IF ₂ change linearly with time.

It is assumed that the input signal of frequency F _{1 has} a power of S, - watts and an average noise power of X watts per hertz and the input signal of frequency F _{2 has} a power of S, - watts and an average noise power of X ' watts per

The output signal of the amplifier 13 is fed to the input of a control loop, the purpose of which is it is to generate an intermediate frequency output signal whose phase and frequency match the phase and the frequency of the input signal are permanently linked. The control loop also contains a mixer 14, an intermediate frequency amplifier 15, a phase comparator 16, a low-pass filter 17, a controlled Oscillator 18, which has a center frequency of 0.5 MHz, and further mixer stages 19 and 20. The output voltage of the controlled oscillator 8 (receiver 24) is via the radio link 26 with the an input of the mixer 19 is connected.

The above-mentioned normal frequency generator (not shown) also outputs signals to terminals 21 and 22 which have frequencies of 30 MHz or (F ₀ + 16.5) MHz, each with a phase angle of zero; these are fed to the phase comparator 16 via a 90 ° element 23 or to the mixer 20.

In the control loop of the receiver 24, the input signal of the frequency F ₀ with the phase angle U ₁ in the mixer 4 with the Gegenkoppiungssignai of the frequency (F ₀ + 30) MHz of the phase M ₁ + / J ₁ , which is present at the output of the mixer 9 and by mixing with the output signal of the controlled oscillator 8 of the frequency 13 MHz and the phase U ₁ + Jl ₁ with the reference signal of the frequency (F ₀ + 17} MHz and the phase angle zero (input 11 of the mixer 9), mixed. The signal at the output of the mixer 4 has a frequency of 30 MHz and an error phase / J _1. This signal is fed to the phase comparator 6 via the intermediate frequency amplifier 5, in which it is phase-shifted by 90 ° (phase quality 12) reference signal of the frequency 30 MHz is compared with the phase angle zero with regard to the phase angle I _1. The direct current component of the signal present at the output of the phase comparator 6 is proportional to sin / J ₁ or to / J ₁ , since the Feh learning phase / J _{1 is} very small. The output signal of the phase comparator 6 is fed to the low-pass filter 7; its output signal is input to the input of the oscillator 8 as a control signal, which generates _{the already mentioned signal of the frequency 13MHz with the phase angle ^ 1} + / J _1; this signal has a power of S ₀ watts and an output of N ₀ watts. The low-pass filter is not shown in detail; However, it is known to consist of a resistor R ₁ in the series branch and a resistor R ₂ and a capacitor in series in the shunt branch (see the article by CJ Byrne, Bell System Technical Journal, March 1962, No. 2, pp. 559 to 602 , especially p. 564, entitled "Properties and Design of the Phase-controlled Oscillator with a Sawtooth Comparator").

In the control loop of the receiver 25, the signal of the frequency F ₀ with the phase angle a ₂ in the mixer 14 with the negative feedback signal of the frequency (F + 30 MHz and the phase angle U ₂ + ß ₂ , which is present at the output of the mixer 20, mixed; the latter signal is obtained as the mixed product (mixer 20) of the reference signal of frequency (F ₀ + 16.5) MHz (input 22) of phase angle zero and the output signal of mixer 19 of frequency 13.5 MHz with phase angle a ₂ + / J ₂ , & 5 which the latter signal in turn by mixing in the mixer 19 the output signals of the oscillator 18 of the frequency 0.5 MHz with the phase angle a ₂ - (I ₁ + ß ₂ - / J ₁ and the oscillator 8 of the frequency 13 MHz and phase angle! U ₁ + / J _1. The signal present at the output of mixer 4 has a frequency of 30 MHz with a phase angle / ^; it is input via intermediate frequency amplifier 15 to phase comparator 16, in which it is ß _{2 is} compared with the 90 ° phase shifted (phase element 23) reference signal (input 21) of the frequency 30 MHz of the phase angle zero. The direct current component of the output signal of the phase comparator 16 is proportional to sin β ₂ or to β ₂ , since the phase angle β _{2 is} very small. The initial signa! the phase comparator 16 is fed to the low-pass filter 17; its output signal is input to the input of the oscillator 18 as a control signal, which compares the already mentioned signal of the frequency 0.5 MHz with the phase angle a ₂ - (I ₁ + / J ₂ - / J ₁ generated; this signal has a power of Sq watts and a noise power of ΛΌ 'watts. The low-pass filter 17 has the same configuration and function as the low-pass filter 7.

Apart from the mixer stages 9, 19 and 20 used here and the coupling between the first and second control loop, each of the control loops is of the type described in the article by W. J a η e ff in "Electrical Communication", Vol. 39, No. 1, 1964, P. 98 to 112, with the title »Satellite-Tracking Receiver«. The function of these control loops is therefore not explained in detail here.

The control loops used in the context of the invention, e.g. B. the one used in the receiver 24 differs from the known, just mentioned in that the output signal of the controlled oscillator 8 is not fed back directly to the mixer 4, but via the mixer 9. This does not change the basic operation of the control loop, but it is used to transpose the intermediate frequency of 13 MHz present at the output of the oscillator 8 into a value such that after mixing this value with the input signal in the mixer 4 a signal of the frequency 30 MHz with the phase (error phase) / J ₁ arises.

The control loop used in the receiver 25 differs from the known above-mentioned in that to provide a signal at the output of the controlled oscillator 18, the phase angle of which is equal to (a ₂ + / J ₂ ) - (M ₁ + A), the output signals of the Oscillators 8 and 18 are mixed with one another in the mixer 19, so that a signal of the frequency 13.5 MHz with the phase angle a ₂ + / J ₂ is produced. The mixer 20 does not affect the basic operation of the control loop, it is only used to transpose the intermediate frequency of 13.5 MHz at the output of the mixer 19 with the phase angle a ₂ + / J ₂ into a value such that after Mixing this value with the input signal in the mixer 14 results in a signal of the frequency 30 MHz with the phase (error phase) / J _2.

The following statements are based on the above-mentioned article by C. J. B y r η e.

If A denotes the gain of the receiver 24 when the control loop is not effective (gain factor of the μ-branch) (which is the control loop

5 6

in Fig. 2), then the lers / ^ ₁ (s) of the control loop contained therein can be used as a linearized negative feedback equation

A '(S) = D-y (s)] «i

«Ω

to be written; where H (s) means the over- s

carrying function of the low-pass filter 7, where / i (s) ge s ² + 2Rm _n S + u? _n

can be written as io

to be written.

H ( _s ) _ _LiJi_L p) The second form of the equation is obtained from

1 + s T ₁ ~ of the first by substituting equations (1) and

_m j _t (2); taking into account that ST ₁ and AT ₂

I ₅ (A large) are large against 1 and by introducing the

T ₁ = (R ₁ + R ₂ ) C parameters of the control loop, that is <·>" as a circular

_{un (} j frequency and R as damping, equation (3) is obtained, where T ₂ = R ₂ C.

20th

(4)

Here s is a (complex) variable that depends on the frequency, and the relationship between and

of this variable and the time variable ί is _(l> j

given by the well-known formula R = ~ ^ τ ~ (5)

25th

r. _ _si The input frequency is a sawtooth as a result

= 1 / (0e ^s ' dr. (J _es Doppler effect, so that one can write:

3 ° U ₁ (S) = 3-. (6)

If in an analogous way with A ' the vers

Strengthening the recipient 25 when ineffective

Control loop (gain factor of the μ-branch) where D is the variation of the input frequency im

draws (the control loop is in Fig. 3 schematically means radians sec ² .

shown), the linearized negative feedback 35 By inserting formula (6) in formula (3)

equation with ■ one obtains

,, D

^{Γ {s] = 1} ^ Xm- ^ ά "1 ¹ λ tu ⁽ " ³ ₄₀ "' ^{S ~ ^{S {s2 + 2R} ' ■ ·" » ⁺ - '" ^] '

_ A 'H' (s) By taking the limit lim / (r) = lim.vF (.s)

~~ s ~ + ~ Ä ~ 'H'ls) mil ί - ♦' / and s - »() makes the static

Mistake, ij to

be written, where H '(s) the supranuims- 45 .. _ -pD

function of the low-pass filter 17. ^lb ~ ~ ,. _t \ ° ^l "

IJ- _(s) _ L ^{+ S} 3-. where D is expressed in Hz sec. ² .

1 + s 7J 'The maximum value of the static error is then

5 °

and 7j and T _{2 are} the time constants of the low-pass filter 17_ 2.tD ",". _t

mean. '- ¹ ~~ _f ., ² _n

It follows that by coupling the

two receivers, in particular the two control - where D _{max is} the greatest frequency variation of the loop-in, the phase difference n ₂ - (I ₁ is the output signal obtained directly Phase error / i ₂ - A occurs. This is compared to From formula (7) it follows that

a measuring method in which the phase angle «,
and «2 are measured separately, of particular 1 1

- · - 13

Advantage. 60 --- = -pp- ^ - (8)

It should now be explained that the signal- '''"' ~ ' ^Ύ '""*

Noise ratio of the output signal, that is that is. "

Output signal of the receiver 25. is particularly good. 'The signal-to-noise ratio:. "Can be written

which means that with the measuring method under '"

difficult noise conditions 65

can. """- ^ ¹ L ₌ ^ L. J _ ^ _. L. ₍₉₎

To do this, the relationships at Emp- -Vt ^ -B r- E ₂ - 1_

catcher 24 considered. The absolute value 'I ₁ ' (.v) of the fault "'G ₁

where means

S, - = power of the input signal for

Receiver 24,

X - mean noise power in watts per hertz, B = the equivalent corresponding to the low-pass filter

Noise bandwidth of the control loop in Hertz, E ₁ = inherent noise of amplifier 3,
E ₂ = inherent noise of the control loop,
G] = gain factor of amplifier 3,
S ₀ = power of the output signal of the

Control loop in watts,
N ₀ = noise power of the output signal of the

Control loop in watts.

By substituting C ₃ = E ₁ -I

£ J

- =. -, (This is

the self-noise of amplifier 3 and control loop together) in formula (9) is obtained

S ₁ -TT

N ₀

X B

(10)

where B is in radians / sec. is expressed.

From the above-mentioned article by CJ B yr η e it follows that if (AT ₂ ) ^{2 is} greater than AT ₁ , which is the case for the low-pass filter, the noise bandwidth B of the control loop expressed in radians / sec

2 B

AT ₂

(Π)

can be written.

Substituting the values from formulas (4) and (5) one obtains

JL - *
2B ~ R, "., '

(12)

and substituting the values from formula (8) gives

JL = 1
2 B [2WR

(13)

Finally, if you put the formula (13) in formula (10) sets in, results

So_

N ₀

XRC,

_4_
D _max

(14)

Must have amplification factor. However, all of these solutions are very complex.

The receiver 25 can be viewed in a similar manner to the receiver 24, and that on Output pending signal can be written as follows with regard to its signal-to-noise ratio will:

^s o _ 1/1.

AD _m

where / J _{4 is} the maximum static error. The Laplace transform for the input signal (see Fig. 3) can be written as

I ' Ia ₂ (t) - O ₁ (t) - / J ₁ (i) 3 * 8 [a ₂ (t) - α, (t)]

D-D '

AD

s ³

It can be seen from this that the signal-to-noise ratio - ^ - of the receiver 24 depends on the values

S ₁ , C ₃ , X, R, ß ₃ and D _{max is} dependent.

The value β ₃ is determined by the desired accuracy; the value for R is chosen accordingly,

z. B. R = -γψ ; the value D is determined by the speed of the satellite and remains constant for the duration of a measurement; the value X ₁ cannot be changed. The signal-to-noise ratio can only be improved by increasing S, -; this means that either the power of the satellite transmitter must be increased or a large antenna must be used. An improvement in the signal-to-noise ratio can, however, also be achieved if the value C _{3 is} reduced, which means that the amplifier 3 and the control loop together have a low level of inherent noise and the amplifier a high level, where D is analogous to D ' , but in with respect to the second control loop.

S '
The signal-to-noise ratio - £ ■ is therefore from AD

addicted; this value is significantly smaller than D and D ', so this signal-to-noise ratio is high

is greater than -J- if the other factors S ₁ -, C ₃ ,

X \ R ' and / J ₄ are equal to the corresponding values of S ₁ -, C ₃ , X, R and / J _3. The signal obtained in this way '
Noise ratio ~ is often so great that it gets through

■ "0

Can be zoomed in on X ' or zoom out S /; this means that less expensive equipment can be used. A larger C ₃ allows the use of a simpler amplifier 13, whereas the use of a less complex antenna 2 reduces S / and increases X '.

A physical interpretation of the high signal-to-noise ratio of the output signal of the receiver 25 can be given as follows: It is well known that a control loop controls the signal-to-noise ratio of a signal, because of the need for readjusting a frequency-variable, weak signal requires bandwidth, which is directly proportional to the frequency variation. By the coupling of the two receivers, especially their control loops, requires the control loop of the Receiver 25 to readjust a much smaller frequency variation than that of the receiver 24. So can also the bandwidth of the control loop for the receiver 25 can be much smaller than the bandwidth of the Control loop for the receiver 24. Due to the narrower bandwidth, there is therefore more noise eliminated so that the signal-to-noise ratio is improved.

In the explanations made so far, it has been assumed that none of the amplifiers 3 and 13 causes a phase shift in their input signals. However, if phase shifts are introduced, the receivers have to be modified as shown in FIG. 4 is shown.
The receiver 42 (FIG. 4) contains an antenna 26, an amplifier 27 which may introduce a phase shift O ₁ , a control loop with a mixer 28, an intermediate frequency amplifier 29, a multiplier 30, a phase comparator 31, a low frequency

809648/1522

pass filter 32, a controlled oscillator 33 with a center frequency of 13 MHz ₅ a mixer 34 and a 90 ° phase element 35. The control loop differs from that in FIG. 1 used only by the presence of the multiplier 30 .. The receiver 42 also contains a second control loop with a mixer 36, a phase comparator 37, a low-pass filter 38, a controlled oscillator 39 with a center frequency of 13 MHz and a 90 ° phase element40. The output voltage of the oscillator 39 is coupled into the antenna 26 via a mixer 41. The normal frequency generator supplies reference signals of the frequency F ₁ = 1 kHz to the input terminals of the 90 ° phase elements 35 and 40, furthermore a reference signal of the frequency (F ₀ +17) MHz to the input terminal 45 of the mixer 34 and a reference signal of the frequency (F ₀ -13) MHz to the Eingängsklemme 46 of the mixing stage 41st

The output signal of the first control loop has a frequency of 13 MHz and a phase angle αϊ + ßi - yi / 2, where y _{x is} the phase angle introduced by the second control loop. If this signal is fed to the second control loop, it can be seen (see also FIG. 4) that a signal of frequency F ₀ + F ₁ with phase angle O ₁ + / S ₁ + y / 2 occurs. This signal is coupled into the antenna 26, which has received the input signal of the frequency F ₁ with the phase angle a _t . It is assumed that the amplifier 27 introduces a phase shift O ₁ , so that two signals appear at its output, one of the. Frequency F ₁ with the phase angle Ct ₁ + O ₁ and the other with the frequency F ₀ + F ₁ with the phase angle O ₁ + Ä + yi / 2 + O ₁ . In the mixer 28, these two signals are mixed with the negative feedback signal of the first control loop, which has a frequency (F ₀ + 30) MHz and a phase angle U ₁ + ßi, - γΙ / 2. The two output signals of the mixer 28 then have frequencies of 30 MHz and (30 - F ₁ ) MHz and phase angle / J ₁ - (S ₁ - yJ2 or - Äi - η these signals are amplified in the intermediate frequency amplifier 29 and then in the frequency multiplier 30 is multiplied so that at its output a signal of the frequency F _{1 appears} with the phase angle ft + yj / 2. The signal obtained in this way is fed to the low-pass filter 32, the output signal of which is input as a control signal to the oscillator 33. The output signal of the oscillator 33 has a Frequency of 13 MHz with a phase angle + ßi - yi / 2. It can be seen that this phase angle is independent of the phase t 1 which the amplifier 27 has introduced.

Claims (2)

Claims: 55 1. Method for measuring the phase difference between two signals received in separate receiving stations in one of the receiving stations, which are transmitted as a single signal from a mobile transmitting station (satellite), for tracking the orbit of the satellite, taking into account the respective phase shifts in the signals caused by the Doppler effect Receiving stations in whose receivers control loops are provided in the manner of a frequency negative feedback, via which the output signal of a phase-controlled oscillator forming the end element of the straight-line branch (μ, branch) is fed into the μ branch for its own control by means of a control signal obtained from a phase comparison, preferably in the mixer stage serving for frequency transposition is fed back (feedback branch), characterized in that the output signal of the phase-controlled oscillator (8, FIG. 1; frequency 13 MHz, phase O ₁ + &) of the first receiver (24) via a Verbi ndung (26) in the feedback branch of the second receiver (25) via a mixer (19), which also the output signal of the phase-controlled oscillator (18) of the second receiver (25; Frequency 0.5 MHz, phase a ₂ -Ci ₁ + ß ₂ - ßi) is fed in, that the input signals of the receivers (24, 25; frequency F ₀ , phase Ct ₁ or a ₂ ) in mixer stages (4 or 14) with signals that are generated by mixing reference frequencies of a standard frequency generator (frequency F ₀ + 17 MHz, phase 0 ° or F ₀ + 16.5 MHz, phase 0 °) and the output signal of the first phase-controlled oscillator (8) or the resulting signal (mixer 19) by mixing the two output signals of the phase-controlled oscillators (8 and 18) are transposed into the same intermediate frequency (z. B. 30 MHz) and that the control signal to be obtained by phase comparison in a known manner for the regulation of the oscillators (8, 18) in the intermediate frequency position (intermediate frequency amplifier 5 or 15) by means of phase comparators (6, 16) in the straight branch by comparison with signals from the standard frequency generator (frequency 30 MHz, phase 0 °). 2. A method for phase difference measurement according to claim 1, characterized in that to eliminate any phase errors introduced by the preamplification (3, 13) for the input signal in the straight-line branch in this one of the phase comparator (31) upstream multiplier (30, F i g. 4) it is provided that a second feedback branch (mixer 36, phase comparator 37, low-pass filter 38, oscillator 39, mixer 41) from the phase-controlled oscillator (33) is provided in the straight branch, the mixer stages (36, 41) of which on the one hand derive from the output signal of the oscillator (39 be and controlled 13 MHz, phase 0 °) that the output signal of the second feedback path (output signal mixer 41) in the - other hand, the output signal of the phase-controlled oscillator (33) or from the output signal of the frequency synthesizer (frequency F ₀₎ of the second Rückführüngszweiges and Receiving antenna (26) is coupled. For this purpose 2 sheets of drawings