DE746192C - Transmission method with frequency modulation - Google Patents

Description

"The invention relates to a transmission method with frequency modulation, in particular one that where two or more signals are sent on the same carrier frequency. The invention is based on the object of eliminating interference as well as possible in a to achieve such a process.

One of the great advantages of using frequency modulation in the transmission of high-frequency signals is the reduction in the reception of undesired interference currents. This advantage of frequency modulation over amplitude modulation is particularly evident when the shift in the carrier frequency is of the order of magnitude of approximately five times the amount of the highest frequency to be transmitted. ^; *. -

It has been proposed to modulate two or more signals by modulating a single one Transmit carrier wave. This was done by having a main support shaft and a or several subcarrier waves were modulated each with a signal to be transmitted, wherein the modulation of the main carrier wave is frequency modulation and that of the subcarriers were either amplitude or frequency modulation. The main carrier is then additionally modulated by each of the Frequency modulated subcarriers. It has now turned out that, to the highest possible To achieve interference elimination on the subchannels thus formed, the frequency of the different Subcarrier waves have a certain relationship to the frequency shift generated in the process of the main bearer must have.

For a more detailed explanation of the invention, reference is made to the drawing, in Fig. Ι and 2 show a frequency modulation transmission system, Fig. 3 and 4 show a modification of the same and Fig. 5, 6 and 7 show certain diagrams that show the mode of operation of the system shown in Fig 1 to 4 correspond to the system shown.

In Fig. Ι is a carrier wave oscilloscope with 1 " lator, the output oscillation of which is fed to a frequency modulator. the Output voltage of this frequency modulator, according to certain desired Signals is frequency-modulated, a force amplifier 3 and from there an antenna 4 forwarded. The various signals to be transmitted are 'sent to the system via the channels 5,6 and 7 supplied. It is assumed that these signals come from different speech or music frequencies. The signal 1 reaches the input via circuit 5, filter 8, amplifier 9 of channel 1 and conductor 10 of the frequency modulator 2, which makes it a frequency modulation! the one from the antenna broadcast carrier wave.

The signal 2 reaches an amplitude modulator 11 via circuit 6, in which it modulates the output oscillation of a carrier wave oscillator 12 of channel 2. This modulator 11 is intended, for example, to generate amplitude modulations of oscillations of the frequency of the oscillator 12 , which are fed via a filter 13 and an amplifier 14 to the circuit 10 and from there to the input of the frequency modulator 2. As a result, the frequency of the carrier wave of the oscillator 2 is modulated by the carrier wave generated by the oscillator 12, the amplitude of which is modulated in accordance with the signal 2.

The signal 3 passes through a channel 3, which is similar to that through which the signal 2 is supplied, and an oscillator 15, an amplitude modulator 16, a filter 17 and an amplifier 18, the frequency of the carrier wave of the oscillator 1 is further modulated by oscillations of the oscillator 15, the amplitude of which accordingly the signal is modulated. The filters 8, 13 and 17 are of course sized so that they only use the frequencies of their corresponding Let channels through.

Fig. 2 shows a receiver suitable for receiving the transmitter according to Fig. 1. It consists of a high-frequency amplifier 21, to which the recorded vibrations are fed from the antenna 20, a mixer 22 in which the amplified high-frequency vibrations of the local oscillator 23 are superimposed to generate an intermediate frequency, which via an intermediate frequency amplifier 24 and an amplitude limiter 25 to a frequency amplitude converter 26 arrive, through which the ^ frequency changes of the received carrier wave are converted into amplitude changes. In this way, all of the currents fed to the modulator 2 via the circle 10 in FIG. 1 are reproduced on the conductor 27 in FIG. The signal 1 then passes through a band filter 28 to the output circuit 29 of channel 1.Currents at the frequency of the oscillator 12, together with their modulation sidebands, are passed through a band filter 30, which is similar to the filter 13 in FIG. 1, to a detector or rectifier 31 reinserted, whereby the signal 2 appears in the output circuit 32 of the channel 2. Oscillations at the frequency of the oscillator 15, together with their modulation sidebands, are likewise fed to a detector or rectifier 34 via a band filter 33, as a result of which the signal 3 appears in the output circuit 35.

Before the relationships between the various carrier wave frequencies of the Systems according to Fig. 1 and 2 are discussed in order to enable extensive troubleshooting in To achieve the various channels, the systems according to Fig. 3 and 4 will first be described will. go

The system of Figures 3 and 4 is similar to that of Figures 1 and 2, except that the channels for signals 2 and 3 ^{contain frequency modulation of their respective L T} subcarriers rather than amplitude modulation. In Fig. 3 the output oscillation of the oscillator τ is fed to the carrier wave input of the frequency modulator 2, the output voltage of which reaches the antenna 4 via a force amplifier 3. _ίΟ ο

The channel of signal 1 is identical to that of signal 1 according to Fig. 1 and exists from the band filter 8, the amplifier 9 and the circuit 10 leading to the signal input of the frequency modulator 2 leads.

The carrier wave for the channels of signals 2 and 3 is supplied by an oscillator 36, whose output oscillation is fed to a frequency modulator 38, whereby its Frequency is modulated according to signal 2 hq. The output voltage of this frequency modulator is reduced in frequency by a mixer 39 in which it is superimposed with the vibrations of an oscillator 39 to generate a low frequency carrier wave. This lowered frequency together with their sidebands is then passed through a band filter 41 and an amplifier 42 is fed to the circuit 10.

The output oscillations of the oscillator 36 arrive in the same way a frequency modulator 43, thereby making them

be frequency modulated according to the signal 3. The output voltage of this modulator is then reduced in frequency by the mixer 44 in which it is with the Vibrations of an oscillator 45 are superimposed. The degraded carrier wave becomes with their sidebands then through a band filter 46 and an amplifier 48 to the circuit ίο fed. Modulate this way

«O these carrier waves, which are frequency-modulated by their corresponding signals 2 and 3, the output oscillations" of the oscillator ι in frequency.
Fig. 4 shows a receiver for use in conjunction with the system of Fig. 3. It is identical to the receiver of Fig. 2 except that the rectifier 31 of Fig

Output voltage is fed to a frequency amplitude converter 50, whereby the frequency-modulated oscillations from the frequency of the output voltage of the mixer 39 are converted into amplitude changes and fed to the circuit 32. This Circle naturally reproduces signal 2. In the same way is the rectifier 34 the Fig. 2 replaced by an amplitude limiter 51, the output voltage of the Freqüenzamplitudenwandler 52 is supplied, whereby the signal 3 is simulated and the circle 35 is fed.

To consider the problem of eliminating interference in the channels through which the Signals 2 and 3 are transmitted, the instantaneous value of the frequency of the The carrier wave emitted by the transmitter according to Fig. 1 can be represented by the following equation:

ω = CU ₀ + A sin a _x t -f- B (r -f- k. ₂ sin a. ₂ t) cos bt + C (1 -f- A ₃ sin a _a t) cos et

(i)

where ω = 2nf- and f is the instantaneous value of the frequency. ω ₀ = 2π / ₀ , where / _{0 is} the frequency of oscillator 1. A, B and C are the individual frequency shifts caused by signal 1 and the subcarriers on which signals 2 and 3 are modulated; a _t , a ₂ and a _s are the corresponding signal frequencies; k ₂ and k _a

co = (U ₀ -f- A cos a _x t - \ - B cos (U -f-

in which the expressions ω, ω ₀ , A, B, C, a _it a ₂ , α _Ά , b, c and t are the same as above · and P ₂ and P _{3 are} the phase shifts that their respective sub-carriers differ from the Signals 2 and 3 are pressed.

It should now be considered to what extent, for example, channel 3 is susceptible to interference caused by unwanted signals, stray electromotive fields, static discharges and the like. It should also be assumed that channels 1 and 2 are unused, d. H. that no signal · in channel 1 and no signal on a subcarrier is present in channel 2. In addition, the subcarrier in channel 3 should also be unmodulated be. These assumptions can be made for any of the systems mentioned, and make the following considerations for

5 "both systems too.

The frequency transmitted by the transmitter according to Fig. 1 or 3 is then

are the percentages of modulation of the two subcarriers; b and c are the angular frequencies of the subcarriers, and t represents time.

The instantaneous value of the frequency of the currents emitted by the transmitter according to Fig. 3 can be represented by the following equation: _Qo

ω = ω ₀ + C cos et

(3)

since all other terms of the two equations (1) and (2) are below those assumed above Falling out of conditions.

The _# voltage generated in the antenna of the receiver can be expressed by the following equation:

(5)

If the value co given by equation (3) is inserted into equation (5) and this equation is integrated, one obtains:

P ₂ sin a ₂ t) - \ - C cos (et - \ - P ₃ sin a _a t)

e _s = S sin Φ
where S is the amplitude and

Φ = [ω dt

₀ t- \ sin et

Substituting Φ into equation (4) one gets:

e _s = S sin I ω ₀ t -J- -— sin et j

(6)

This equation represents the current that will flow into the receiver's antenna during the Passing the above conditions is generated.

It should now be assumed that an interference EMF e _u also influences the receiving antenna, the amplitude of which is N volts and the frequency of which differs from the received antenna

Carrier frequency by -

kHz differs.

This interference EMF can be expressed as follows:

e " = A ^T sin [K + μ) f]

(7)

• The total EMF induced in the antenna, which is to be denoted by e _r , is then the vector sum of e _s and e ".

These quantities are shown vectorially in Fig. 5, in which the vector e _{s is drawn} at an angle α to the horizontal and the vector e _{n is drawn} at an angle β to the horizontal and the vector e _{r represents} the sum of these two vectors, where

oc = - sin et from equation (6) (8)

and

/ 9 = / ti

of equation (7) (9)

From the geometry of this vector diagram one obtains the relationship:

sin δ Ν

in which <S represents the angle between the vectors e _s and e _T.

The strength of the interference currents should not be greater than half the strength of the received Signal current can be assumed. A received interference current of such strength would be in the received signal is practically incomprehensible to an ordinary amplitude modulation system make and a noticeable

although not necessarily causing objectionable disturbance in a frequency modulation system. For the present purpose it is sufficient to assume that the interference current is less than half as strong as the desired signal current.
From Fig. 5 you can see that the angle <5

N can never be greater than 30 °, since -W never

is greater than - is. For angles of 6 smaller than 30 ⁰ can be

sin δ = δ and

cos δ - ι can be assumed.

. If these quantities are included in equation (io)

Ni
set and - ^ - = - set, then we get:

δ = -L sin (oc - β) Γ- ~ 1 (II)

² l ^ + J-costa-flJ

The quantity - · cos (<x - ß) is always the same

or less than-

Therefore, the training

pressure in brackets in equation (11) as Are expressed in power series, and equation (11) is given the form:

δ = sin (α - β) ι - - cos (α - β) + ~ - cos ² (α - β) + ...

= --- ■■ sin (a --- ß) - -g- sin 2 (oc - ß) + (12)

The resulting signal voltage e _r has; pull axis, which is equal to α - δ . From an instantaneous phase angle with the equations (8) and (12) this angle can horizontal line in Figure 5 are calculated as arbitrary loading as follows:. ^'I0 °

oc - Ö - - sin et - \ sin (ß - α)

sin 2 (ß - α) 4- · · ·

(13)

From (8) and (9)

β - α = μ t sin et

C fit + - sin (- et)

Substituting this quantity into equation (13) gives:

S ^ «- = - δ = —- sin ct- \ sin μί - \ sin (- et) ■ - sin

ι I. aC.
- sin 2 μ t H sm 1

■ Ct) \ + ... (I ₄ )

By using the Jacobi expansion formulas for the sine terms and by designating / "(-! As a Bessel function of the order ti and the argument—

. _Δ C

becomes, if one sets -— = m

■ δ - m sin et - { - [J ₀ (ni) sin μί = -2 J ₁ (m) sin et cos / </ 4- 2 J. ₂ [m) cos 2 et sin μί

.8th

[T ₀ (2 m) sin 2 μ-t - 2 J ₁ (2 m) sin et cos 2 μt - \ - 2 J ₂ (2 m) cos 2 ct. sin 2 μt. · ..]

(15)

From this expression it can be seen that the angle α - δ changes to an extent that · from a number of different frequencies ^c > u, c + μ, 2 C + μ, 2 μ, c + 2 μ, 2 ε + 2 μ etc. depends.

The band filter 33 of the receiver according to FIGS. 2 and 4 only allows the subcarrier and its frequency spectrum to pass, which includes its upper and lower modulation sidebands. Only the frequencies c, c + μ and c ± 2 μ are covered by this spectrum, and the terms of equation (15) which contain the other frequencies mentioned above can be neglected.

The expression then becomes

α - δ = m sin et - J ₁ (m) sincicos / ii-l J ₁ (2 m) sin et cos 2 μι

This expression gives the phase angle

of the vector e _r as a function of time. Around

To get the frequency change of the vector e _r , this expression is differentiated with respect to time, and one gets

-τ (α - ~ δ) - mc cos Ct-J ₁ (m) [c cos μί cos et - μ sin μι sin et]

(17)

- \ J ₁ (2 m) [c cos 2 μί cos et - 2 μ sin 2 μΐ sin et]

The first member of the right-hand side of this equation represents the subcarrier with the frequency c , the second member a modulation vector of this carrier with the frequency μ - and the third member a modulation vector with the frequency 2 μ.

The first term of equation (17) can be represented by a horizontal vector mc, as in Fig. 6. Likewise, the term c J ₁ (m) cos μ t cos et can be represented by a horizontal vector, the maximum length of which is equal to c J ₁ (m) , but which is

during a period of the frequency μ changes in length like the cos μ t . This vector is ■ denoted in Fig. 6 with c J ₁ (m) .

The term // Z ₁ (Wi) sin μ t sin et can be represented by a vertical vector,

40 'whose maximum length is equal to μ J ₁ (m) , but which changes in length like the sin μ t during a period of the frequency μ . This vector is denoted in Fig. 6 with μ J ₁ (m).

* 5 The vector sum of the quantities (CJ ₁ (In) cos ^ ai) and (μ J ₁ (wi) sin ^ i) results in a; new vector M, the end point of which describes an ellipse, which is shown in Fig. 6 with dashed lines. The major axis of this ellipse has a

So length is equal to 2CJ ₁ (Wi), while the minor axis has a length of 2 μJ ₁ (m) .

Since the equation (17) is a frequency equation the vectors of Fig. 6 are frequency vectors. However, since the frequency amplitude converter a -linear conversion of the frequency changes into voltage changes, this diagram can be seen in Fig. 6 can be viewed as a representation of the voltage vectors, namely those voltages occurring at point 60 in Fig. 2 or at point 61 in Fig. 4.

The resulting vector from the carrier vector wc and the modulation vector M is shown by the vector W in FIG.

The receiver in Fig. 2 should now be considered first. According to Fig. 6, the vector W changes its length between a maximum \ 'on (mc + c J _x (m)) and a minimum of (mc - cJ _t (m)) and is

c J ₁ m

hence amplitude modulated by In other words, the

• 100%.

mc

unmodulated

Subcarrier c, which is generated by the oscillator 15 of Fig. Ι, is received at point 60 of Fig. 2 with an amplitude modulation of the frequency μ and a modulation depth which is given by the expression (18) and which is received by the Interference EMFs are generated when these interference EMFs are half as strong as the desired signal EMF.

Let us now consider how the receiver of Fig. 4 ^{responds to the voltage represented by the lt> 5} vector W , which appears at point 61 in Fig. 4. The limiter naturally removes any differences in amplitude of the vector W. However, the phase differences of the vector W form the variable frequency from which the signal is generated by means of the frequency-amplitude converter. The instantaneous angle between the vector W- and the vector mc is Θ. ■

If the approximately maximum phase difference between the vector W and the vector mc is denoted by & _m , then this results for small phase shifts

mc

(19)

The phase change takes place at the speed // and is approximately sinusoidal. thats why

Θ =

μ J ₁

mc

sin μΐ

(20)

The resulting frequency change is then differentiated by equation (20)

d Θ β * JAm). . .

-COSjM.i (21)

German

mc

From equation (2), it follows that P _{3 represents} the phase shift which the signal 3 impresses on its subcarrier, and that P ₃ a _{A is} the frequency shift which is generated in the frequency of this subcarrier by the desired signal. The relationship:

mc

P ₃ «

100

(22)

₃ «3

therefore expresses the relationship between the strength of the undesired disturbance and the desired signal.

From equations (18) and (22) goes

Now we can see that the perturbation is proportional to the size J ₁ (m) in both cases. Fig. 7 shows the function Z ₁ (to) against the quantity m

plotted, the curve being plotted according to tables of the Bessel functions.

It can be seen from this curve that the quantity m has a number of values for which the quantity J ₁ (m) is equal to zero. The size m is

the ratio I - J of the frequency shift

of the main carrier versus the subcarrier frequency. Therefore, if this ratio is made so large that the size J ₁ (m) is equal to zero, the disturbance is greatly reduced. The first three values for m where the size Z ₁ (m) is equal to zero are

ni = 3.83- m = 7,015, m = 10.17.

Accordingly, if the subcarrier frequency is e.g. 50 kHz, the interference is greatly reduced,

if the shift of the main carrier frequency is equal to 50 * 3.83 = ig 1 kHz or 50-7.015 = 351kHz or 50 x 10.17 = 508kHz is. For practical reasons, however, the first of these values, 191 kHz, will be chosen, although the other values are also used successfully for troubleshooting can.

In the above consideration of equation (17), the last term was neglected. This member represents a disturbance member with the frequency 2 μ , the amplitude of which, however, is only about V _{4 of} the amplitude of the component which the second member represents. In general, the perturbation that this term contributes is small compared to that that the second term contributes, so that it can be neglected. The size of this term can be taken from Bessel's functions, from which one finds that if m = 3.83, as stated above, then J ₁ (2m) = 0.173. If this value is introduced into the last term of equation (17) and multiplied by V4, it is found that this term is completely negligible.

From the steepness of the curve in Fig. 7 in the vicinity of the points of intersection with the axis m it is seen that the invention should be closely adhered to the above angege- g ₀ surrounded values of m fairly \ Verden for reducing the disturbance in accordance with, and if deviations therefrom should be necessary for practical reasons, these should not be more than 10% ^{b y} the values indicated then.

Claims (2)

Patent claims: i. A process for Nachrichtenübertra supply with a low susceptibility to interference, is frequency modulated on a main carrier wave which _go with at least one sub-carrier wave, and each sub-carrier oscillation is amplitude or frequency modulated with a signal. characterized in that the ratio m of the change in frequency of the main carrier caused by a subcarrier to the frequency of the subcarrier is chosen so that J ₁ (tu) is equal to or almost equal to zero, J ₁ (m) being the first order Bessel function with the argument m is. 2. The method according to claim 1, characterized in that the value 3.83 or 7.015 or 10.17, in particular the first-mentioned value, is selected for the ratio m i " _5. Definition of the Anmeldungsgegen- _(ιο state of the art the following documents have been taken into account in the grant procedure: U.S. Patent No. 1 941 069: French patent .. - 493 (> ( > o: _{αι5 USA.} -Patent - 2 104 012. 1 sheet of drawings