DE2242514A1 - MULTI-CIRCULAR SUB-CRITICAL HOLLOW CONDUCTOR TAPE - Google Patents

Description

Dipl. Phys. Leo (Dhul

7 Stuttgart 3o

Short street 8

G.F. Craven-D.W. Stop-C, K.Mok 24-3-Ί

ΙΜΕΕΙΤΑίΕΕΟΪΓΑΙί STAHDAED EEECIEIC COEPOEAiEIOlT, HE ¥ YOEK

Mehrkrelsiger subcritical Holill pus band pass

The invention relates to a circular waveguide bandpass filter as it is described in D ¹ E-OS 1 54-1. .

IJriter a unterkritivgolien Holilleiterbandpaß mrd in of the above-mentioned publication and in this application a waveguide operated by its (limit frequency) in which only damped Η waves occur can, which is terminated with a capacitive reactance at the central frequency of the pass band In the positive imaginary resistance of the position of the Waveguide corresponds.

August 14, 1972
vo / f £

BATH ORIGINAL

G. F. Craven 2'I-3-1 - 2 -

A detailed description of such subcritical hollow conductor tape passes can be found in a Article in "IEEE Transactions on Microwave Theory and Techniques, Volume MTT -19 No. 3, March 1971."

In the case of such subcritical bandpasses, the hollow conductors are designed so that their cut-off frequency is above the operating frequency. In the case of waveguides for the fundamental oscillation, the propagation of advancing waves ceases below the cut-off frequency and one then speaks of a damped fundamental oscillation. Waveguides in which the fundamental oscillation is damped have a positive imaginary wave resistance (JZ ₀ ) for an H, wave and a real propagation constant Cf) and therefore never behave practically like a pure reactance. If you add an obstacle to the end of a short section of length 1 of such a waveguide, which has the conjugate (capacitive) reactance at the center frequency of the bandpass, which is below the cutoff frequency, then the power applied to the input at this frequency is complete transmitted through the section, since a cavity is formed, the center of which is the capacitance.

Un t ο rcriti sohe Hoh L1e it er bandρässο s ind we s enti ch small no c and lighter than HoIlL Le Lter, in which progressive We.LLon form. Theoretically, there is no limit to the size that can be reduced, but in practice the reduction is by that. Loss υ limited. Subcritical HohlJ.s) iterbandpiuiso. Are in

U)) I) N) / 08 I J BAD ORIGINAL

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generally ο j 3 "to o- _f 5 times narrower than the" well-known waveguides for advancing wool Waveguides for progressive lines * This reduction in length becomes smaller * if the bandwidth is reduced * For example, a filter with a bandwidth of "1 fo " at an operating frequency of 4 GHz is made up of white hollow conductors Length of the cavity about 4 * 5 cm j whereas the cavity of the waveguide tPyp Wd-ISa is about 5.5 cm (/ Vg / 2) »With smaller bandwidths the reduction in length is even smaller * Mes results from this) because the cavity of a common is hollow conductor no longer than / Sg / 2 _s whereas it in the subcritical Hoülieitern no defined length limits are * Bie bandwidth 'is gedooh fast small SCLA with increasing Honlraumlänge Γ as sinh ^ lbei large values increases rapidly »

One therefore achieves bandwidths smaller than. 1 fo no substantial reduction in length with subcritical waveguides, as described in the publications cited above, but a substantial reduction in cross-section can * - '., -., .. """■

It is therefore the object of the invention to provide one possibility specify to reduce the length of subcritical waveguides «'-

BATH ORIGINAL

G.F. Craven 24-3-1

According to the invention, this object is achieved in that Approximately in the middle between the resonators there is a susceptance value is arranged.

The invention will now be based on exemplary embodiments explained in more detail. Show in the drawings

Fig. 1 shows a multi-circuit subcritical waveguide bandpass with inductive load in the middle between the resonators,

2 shows a cross section of one of the resonators,

3 shows an inductive rod in the bandpass filter,

Figure 4a

and

4b shows two different equivalent circuit diagrams of a length section a subcritical waveguide bandpass,

Fig. 5a,

5b and

5c different equivalent circuit diagrams

a subcritical waveguide bandpass with transverse blind conductance,

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FIG. 6 shows the transmission curve of the bandpass filter according to FIG. 1,

Figure 7a

and

7b shows the equivalent circuit diagram of an unloaded subcritical waveguide bandpass with normalized impedances and the equivalent switching. '' image of a waveguide bandpass loaded with a susceptibility value, with normalized impedances,

8 shows an inductive pair of rods in a subcritical waveguide bandpass,

9 shows the transmission curve of a subcritical waveguide bandpass according to FIG. Λ , but with a reduced length,

Fig.io the dependency of the bandwidth on the coordination with inductive loads of different strengths.

Fig. 1 shows a six-circle Ichebyeheff bandpass filter with a ripple of 0.05 Db and a center frequency of 7587 GHz, which is constructed from a Zupferrohrleiter Λ (WR62). The inner limit of the length of the square is 0.0622 inches. The bandpass filter has 2 flanks at the ends and contains 6 resonators 3. · Each

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G. F. Craven 24-3-1 - I -

Resonator consists of a quartz rod 4- (Fig.2) with a diameter of 8 mm. This quartz rod protrudes into the waveguide and is by means of a Screw / nut assembly 5? 6 adjustable. Everyone Rod 4 is adjusted to create a capacitive obstacle that conjugates the required Represents reactance.

In the middle between the resonators are transverse inductances, each consisting of an inductive rod 7 made of copper wire with a diameter of 0.05 inches. Each inductive rod 7 is offset with respect to the longitudinal center line of the waveguide. The distances d (FIG. 3) between the individual bars are: d ₂ = d ₆ = 0.26 inches; d ^ = dr = 0.242 inches; and d ^ = o, 24o inches.

Palis required can still trimmers on the other Side of the center line.

The total length of the band pass is 7 ₅ 6o3 inches. The lengths I ^ to Ir ₇ between the resonators are;

1 ^ ₁ = 1 = 0.616 inches; I ₂ = I ₆ = 1.208 inches; 1 = 1 = 1.313 inches and I ₄ = 1.329 inches.

The bandpass is 25% shorter than a subcritical one Bandpass without inductive loading.

In the article mentioned in the introduction it is stated that the equivalent circuit diagram of a length 1 is subcritical Bandpass, which is shown in Fig. 4a, can be redrawn so that there is an impedance inverter

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GI ¹ . Craven 24 - 3 - 1 - 1 -

contains, which has a real wave resistance X _Q si. It is

r _ 120 3Pb

^L o "

-1

T = χ

The remaining cross elements X tantir! "Form a resonance circuit with suitable capacitances, as shown in Fig. 4b. If a shunt inductance is inserted in the middle between the capacitances, then the equivalent circuit diagram corresponding to Pig. 4a is shown in Fig. 5a, where X _Q / B is the additional shunt inductance and 1 'is the new (reduced) length between the capacitive rods.

The calculation of B and I ¹ is now derived. For this purpose, the T-element, which is shown in the dashed rectangle in Fig. 5a, is first converted into a JT-element (dashed rectangle in! Fig. 5 ~ b) using the T-jf transformation.

X ₀ sinli 4 ^ - (2a)

= Parallel impedance of

₂ tanhJl-

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G.F. Craven 24-3-1 - * -

then _o

X _Q = 2X. + 7-a I -Ä-o

= X ₀ ET sinh * γ- + sinh ² ^ - (B + 2 tanh Έη £ - ) I = X ₀ (sinh TV + B sinh ² yi '), (3a)

A ^ = X ₁ + ^ ₂

= Σ _Λ (sinh

B + 2 tanh

This converts the equivalent circuit diagram according to FIG. 5b into the equivalent circuit diagram according to FIG. 5c, which contains an impedance inverter with the impedance X and remaining shunt inductances X _Q / Y.

With the same bandwidth between the section loaded with the susceptance value and the unloaded section the two inverter impedances must be largely the same be, i.e.

X _a = X ₀ (sinh j-1 '+ B sinh ² -t | ~) = X _Q sinh rl,

it follows from this

B = sinhjl - sinhfl ' _{? (5 &)}

sinh

or B = 2 (sinhfl - sinhfl ')

cosh yi ¹ - 1 (5b)

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Therefore, if the reduction in length is known, B can be calculated from equation (5). Thus, only equation (5) is required to produce the bandpass filter with a reduced length. It is not necessary _{to calculate X Q} / Y as the bandpass is tuned by hand. However, Y can be calculated as follows. If you compare! Ig. 5 "b and Fig. 5c it can be seen that

thats why

Y 1, 1. 1

Ϊ ~ ~ ^ ^ y-IL ⁺ X ~~ ⁺ X ο X coth -J ^ - ba

If equations (3a) and (3b) are inserted into equation (7) and these are rearranged, one obtains

1 + 1 tanh f

Y- = coth Jl '§ -g-, (8)

⁴ 1 + 1 tanh P

FIG. 6 shows the transmission curve of the bandpass filter according to FIG. 1 reduced in length by 25% as a solid curve and the transmission curve of an unloaded bandpass filter as a dashed curve.

It can be seen that the bandwidth becomes slightly smaller as the length is reduced. On the one hand, the lower value of the shunt inductance (X tanh ΥΊ compared to X _Q / Y) results in an increase in the Q quality.

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G.F. Craven 24-3-1 -1ο-

On the other hand, the correction factor is Δ -, -, where

and X = Eesonsoz wavelength,

I +

which corrects the deviation of the subcritical inductance X from the lumped inductance, too small if it is used with X _Q / Y and the result is therefore a larger bandwidth than the calculated bandwidth.

The approximation theory given above is accurate for length reductions up to 25%. For larger reductions, a more precise theory is required, in which the difference between Y and coth V ^- I and the imprecise correction factor:
are.

factor AL to correct for X _Q / Y must be taken into account

The derivation of the equations for the exact theory is relatively simple with the aid of the equivalent circuit diagram according to FIG. 5c, since the results of the calculation can be used for the unloaded bandpass filter. Figures 7a ^{urL (} 3-7b show the equivalent circuit diagrams with normalized impedances of an unloaded bandpass filter and the corresponding loaded bandpass filter. The circuit diagrams are largely identical and only differ in the inverter impedance (X-sinh Yl ,, X) and the remaining shunt inductance ( X tanh ¹ Y ^- I,, X / Y). The equations apply to the unloaded bandpass filter:

(9a)

-11-

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GE ¹ . Graven 24-3-1 - 11 -

22425U

sense

r j £ 1 will

(9b)

> If =

cotYes
Bandlthreite

(1oa)

! For r = 1,

broad

(1o "b)

A direct comparison results in the corresponding expressions for the equivalent circuit diagram Pig. 7b, where the line index for the loaded bandpass filter is used:

sinh

(11b)

where Λγ is the correction factor for the rest Querleiisert T is.

I ¹ Ur r / ^ 1 becomes

-12-

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tanh. for small bandwidth and low load.

For r = 1,

U) L '= 5- ^ 1 (12b)

for low bandwidth and low load.

One difficulty is to find an expression for Δγ that is the difference in the leading edge of X./Y compared to a pure inductance. From equation (8) it follows:

X 1 + 1 tanh 2 = X ₀ tanh ^ l '^ -: (13a)

₀ ^

.1 + S tanhfl ' ^ (J

A correction factor for this equation would be very extensive, since X, _, tanhoKL and B are frequency-dependent.

o β

are pending. Fortunately, this correction factor is not required. The exact theory is only necessary for large reductions in length where large values of B are required. One can therefore approximate with good accuracy

γ ° -2ίΧ ₀ tanhIt ^ - (13b)

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G.F. Craven 24-3-1. - 13 -

A correction factor for this expression can then be obtained without difficulty in a manner similar to "bei the derivative of Λτ · This results in

) ²

This value is of course dependent on the length and at first glance different correction factors appear to be necessary for each cavity. However, since the expression containing the length is small compared to 1, changes in this expression in the denominator have little effect. In addition, since the cavity lengths are approximately the same in a multi-circuit bandpass filter, it is sufficient to use a common correction value ^ ly for. to use the filter that uses an appropriate value for Vl / sinh V ^- I.

Equation (11b) is understandably more complex than equation (4) and contains not only B but also B ^ and B ^ ,. If one assumes that the value for sinh ^ l _{r is} known from a previous calculation for an unloaded filter, then the value sinh / Y-1 for a certain value of the length reduction is also known and the unknown values are the B values, ie the inductive susceptibility values that are necessary to bring about this reduction in length.

First the values B 'from equation (5) are calculated as a first approximation, from which the X values can be obtained using the equation (8).

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These T-values are then put into the right hand side of the equation (11b) and together with 4 Y a new set of B-Verte results. In general these are Values exactly and no further substitution is necessary.

An inductively loaded band pass with a length reduction of 40% compared to an unloaded band pass is largely similar to the band pass in FIG. Apart from the greater reduction in length, the band pass remains essentially the same. However, since larger inductive susceptibility values are required, inductive double rods are used, which are formed from two copper wires 17 (Fig. 8), which have a diameter of 0.05 inches each and which ^{are arranged at a mutual distance d 1} , where dp = dg = 0.26 inches and d = (U = 0.242 inches and d ^ = 0.24o inches.

9 shows the transmission curve of the bandpass filter, the length of which is reduced by 40% and which is also made up of square waveguides WR62.

If a subcritical bandpass is tuned in a certain frequency range, the changes Bandwidth with frequency. Inductive loading reduces this effect.

There will now be the change in bandwidth with frequency first examined with an unloaded bandpass filter. M'än is based on the equation

^W o ^L r (15)

- 15 -

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The equation (15) together with the equation (loa) gives an expression for the bandwidth

Λτ.ί

cosh / Yl \ / ^& r ^{e &} r + 1 y (tanh-γ-Ι _Λ + tanh ^ lj (tanh * l +

Qxv τι jj χ— ι · <jr qr g

i.e.

^WJ cosh / y-1 t / (tanh γ-1 ^ ₁ + tanh * l " ) (tanh '» l + tanh γΙ , _Λ ), I χ »{r— ι tr {r ή r + 1

since the values for g are constant.

Approximately is the bandwidth

f «

This approximation is permissible "since once tanh γ-l itself changes slowly with the frequency and, on the other hand, the index of the counter and the Henner changes below the Cancel each other's roots.

In the case of a multi-circuit bandpass filter, there is a different one for each section with a different length Bandwidth change, as can be seen from equation (16). However, this equation is for cavities with different bandwidths at f uncritical with regard to the length. As a result, one can Bandpass filter in which the cavities differ only slightly, the bandwidth with very good accuracy predict if only one of the cavities is considered using equation (16b). the end Equations (11b) and 12) give the bandwidth for an inductively loaded bandpass filter

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G.F. Craven 24-3-1 - 16 -

bw =. . ",", _{F χ}

If you substitute the Y-values and do a similar one Considered as above, the bandwidth results to a good approximation

^A Y ^f o
bw% -. . tanhfl '(18)

FIG. 1o shows the change in bandwidth as a function of three filters with a band center frequency of 8 2o5 GHz on the frequency. Equation (16b) was used to calculate the 0% curve and the Equation (18) was used for the reduced length bandpasses.

The improvement in the change in bandwidth with inductive loading can be clearly seen.

So far, only inductive loading has been considered, i.e. capacitive loading was not mentioned. the The above theory can of course also be used with capacitive loading, with only one negative The sign for B is to be used. As expected, the effects are the opposite of those of inductive loading. This may seem undesirable, but it is the easiest way to mechanically connect a waveguide a screw that is predominantly capacitive, this type of load is extreme useful to allow tolerances in the lengths of the cavities

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balance. This is mainly required in Cases where excellent operating characteristics are required. In this case it is a very precise one Vote required. The susceptance is very small in this case and the equations of Maherung theory can be used if one provides a negative sign for B. At a Increasing the length of the bandpass mentioned in the example requires a value for B of about 0.1.

5 claims
■ 4 sheets of drawings

309810/0813

Claims (5)

G. Έ. Craven 24-3-1 - 18 - Claims Multi-circuit subcritical waveguide bandpass, characterized in that a susceptance value is arranged approximately in the middle between the resonators. 2. Bandpass filter according to claim 1, characterized in that the susceptance is inductive. 3. Bandpass filter according to claim 1, characterized in that the susceptance is capacitive. 4. Bandpass filter according to claim 2, characterized in that a quartz rod arranged outside the longitudinal center axis is provided as the inductive load. 5. Bandpass filter according to claim 2, characterized in that a quartz rod is provided on the left and right of the longitudinal center line. 309810/0813 Blank page