Construction of a polarization sensitive planar antenna for microwaves in the centimeter range

Student’s name: Vassilios Papathanakos Supervisor’s name: Prof. Suzanne Staggs

Physics Department, Princeton University October 2002

Table of contents: A. Introduction B. Design of the Antenna C. Experimental Techniques:

I) Microwave production and measurement II) Microstrip milling

III) SMA connection: a) Normal-set method

b) Parallel-set method IV) Microstrip coupling:

a) Hole coupling method b) Bridge coupling method

V) Final setup: a) Antenna b) Support rack

D. Measurements: I) Angle dependence – polarization characteristics

II) Distance dependence – beam characteristics III) Frequency dependence – band characteristics E. Conclusion F. References

A. Introduction One of the most important sources of information on the physical conditions prevailing during the early age of the universe is the cosmic microwave background (CMB) radiation. This radiation is a remnant of the very high temperatures that were present at the earliest stages of the universe's evolution and has been traveling through space ever since the temperature dropped enough to allow the electrons and the protons to form stable atoms.

Although the property that led to the experimental discovery of the CMB radiation was its isotropy, the first careful study investigated the frequency spectrum. Recently, a series of experiments involving satellite observatories proved that CMB radiation is highly isotropic; this is generally considered to offer the best proof that the matter distribution in the early universe was highly homogeneous. However, other properties of the CMB are of interest as well. Most notably, the presence of non-zero polarization in the CMB radiation can be used to test current views on the conditions present immediately after the Big Bang; for that reason, the evolution of efficient methods of measuring the CMB radiation polarization is of great significance (see e.g. Leitch et al – Ref. 3).

In order to measure the polarization of radiation in the microwave region three methods can be used. In the first method, one splits the incident radiation in two beams, each of which contains only one polarization component of the original beam, then one uses two polarization-blind receivers (such as bolometers) to measure the intensity of both component beams’ independently, and then differences the two. The second method consists in using a polarization-sensitive receiver to measure the intensity of each polarization component of the incident beam, either consecutively or simultaneously with the same receiver. A third method is to measure the polarization parameters directly by generating EnEp, the product of field components.

The purpose of this experimental project was to investigate the use of the second method to measure the polarization of a microwave beam. For this reason, an antenna design was chosen with the hope it would allow the simultaneous measurement of the two polarization components. The emphasis of this work was mainly in understanding the underlying physical principles and evolving new techniques rather than optimizing the experimental configuration. For that reason, although the original antenna design was intended for use at frequencies around 500GHz, it was modified for use at frequencies around 10GHz, since lower frequencies designs are easier to implement.

Consequently, and before the construction of the actual antenna circuit took place, a number of tests were performed to develop an understanding of the physics of microwave propagation and detection and to investigate the appropriateness of various techniques. Following these tests, a prototype antenna circuit was constructed and measurements were taken to study its polarization, beam and band characteristics, leading to the conclusion that the constructed antenna had good polarization sensitivity and satisfying beam and band characteristics.

B. Design of the Antenna The design adopted for the antenna is of the “Dual-Polarized Cross-Slot” type and it consists of two pairs of parallel microstrips. Microstrips are a type of planar microwave transmission line and consist of a dielectric plate with a thin layer of conducting material on each side. The lower layer extends usually over the entire surface of the plate and is taken to be the ground plane. The upper conducting layer, usually consisting of a union of rectangles, is chosen with the particular application in mind; a simple example is shown in Figure 1.

with conductor on lower surface

Figure 1. Generic microstrip architecture.

In the adopted design, all microstrips that compose the receiver of the antenna are of the same length L and the two pairs are normal to each other as shown in Figure 2. The distance between the two microstrips in the same pair is equal to S=L/2, while their width W is taken to be much smaller than their length: W~L/10.

Figure 2. Antenna design and currents for normally incident EM wave with polarization along the y-axis. The directions of the surface currents on the microstrips for an incident wave of polarization along the y-axis are also shown in Figure 2. The complexity of the geometry

does not permit a full theoretical analysis of the antenna; however, the use of symmetry principles and approximations lead to some understanding of the underlying principle of operation. First, consider a polarized plane wave arriving on a slot lying normal to its wavevector and parallel to its polarization vector. The resulting electric field and voltage distribution inside the slot will have a sinusoidal dependence and the leading mode will exhibit peak values at the points at 0.25L and 0.75L along the slot length; the current distribution will exhibit nulls at the same points. For that reason, the crossing of the two pairs of slots at these points will produce only a small perturbation in the current flow. Next, consider a plane-polarized plane wave arriving on a slot lying normal to both its wavevector and to its polarization vector. The induced current distribution will exhibit nulls at the midpoint of the slot. Thus, when a plane-polarized plane wave is normally incident at the two pairs such that its polarization vector is parallel to the one pair and normal to the other, a signal will be detected only at the midpoints of the slots in the second pair. Since the two pairs are polarized in normal directions, it is thus possible to measure simultaneously the two polarization components of the incident EM wave and the antenna is called dual-polarized. The actual distribution of currents and the optimal dimensions of the antenna cannot be determined analytically. In practice, computer programs are used to simulate the fields and the currents and to find the antenna design that will optimize the detected signal under certain constraints. In the present experimental project, the aim was rather to investigate the possible techniques in constructing the antenna than to optimize them. For that reason, the dimensions in Goutam Chattopadhyay’s Ph.D. thesis (Dual Polarized and Balanced Receivers at Millimeter and Submillimeter Wavelengths – Ref. 1) were used, modified by the following scaling argument. The antenna in Ref. 1 is designed to work optimally for frequencies around 500GHz. The length of a microstrip should be of the same order of magnitude as a wavelength of the incident radiation. Taking the relative dielectric constant of the underlying dielectric (SiO) to be εr=11.8, the wavelength is calculated to be about λ=175µm, which is close to the dimension of L=200µm actually employed in Ref. 1. Since a different dielectric (G-10) as well as a different typical frequency are used, the antenna length should scale approximately as L=L0(f0/f)√(εr0/εr). Taking f=10GHz and εr=2.5, this last relation gives approximately L=2.2cm. It should also be noted that the microstrips constructed for testing the various techniques usually had a width of approximately 0.43cm, which corresponds to an impedance of 50Ω, as calculated from the corresponding formulas in Microwave Engineering (Ref. 2) by David M. Pozar (pp. 162). On the other hand, the microstrips used in the receiver circuit itself had a width D=L/10=2.2mm.

C. Experimental Techniques: I) Microwave production and measurement In investigating the techniques to be described in the following sections, the main property of interest is the signal loss when a microwave signal goes through a channel and its dependence on the input signal power and frequency. The source of microwave power was an HP 8620C Sweep Oscillator together with the HP 86290B RF Plug-in (Picture 1). This oscillator can produce either a microwave signal of constant frequency or a signal with a frequency that sweeps a range of values in a specified way. During the measurements only the first mode of operation was used. The frequencies can be chosen in the range 6-12GHz by the main knob (Picture 1: A), while a fine-tuning knob (Picture 1: B) allows more precise control over a frequency range of +300MHz (Picture 1: C). The signal input power is controlled through the RF Plug-in (Picture 1: D).

F

D

E

B

C

A

Picture 1. The HP 8620C Sweep Oscillator (bottom left) with the HP 86290B RF Plug-in (bottom right) and the digital multimeter (top). The output of the oscillator (Picture 1: E) was used as the input to the microwave circuit under study through a flexible SMA cable. In order to study the signal loss through a particular channel, a crystal diode detector was connected to the appropriate output in order to rectify the signal. An attenuator connected straight to the crystal detector was also used to check the consistency of the measurements and to estimate the signal loss due to impedance mismatches and connection losses. The output of the crystal detector or the attenuator was fed through a coaxial cable to a digital multimeter to measure the DC voltage (Picture 1: F). The general procedure for computing the signal loss for a particular circuit configuration consisted in first measuring directly the voltage output of the frequency generator (also called the reference channel) and then interjecting the circuit and measuring the voltage output again; this was repeated for a few different values of the

input voltage. Then the data were plotted and a linear least-squares fit was performed in order to compute the signal loss as the slope of the straight line.

In order to check the consistency of the measurements, a second pair of measurement was often taken with the additional interjection of the attenuator. The discrepancy between the sum of the signal loss for the circuit and the attenuator respectively and the signal loss for the circuit with the attenuator was found to be relatively small and could be attributed to additional signal loss due to the impedance mismatches between the various components as well as due to contact resistance.

Another issue of concern was the precision of the frequency generator. In order to investigate it, three series of measurements were performed varying the fine-tuning knob while the main knob was fixed at some frequency. The first two sets of measurements (Tables 1 and 2) were taken in order to check the relative precision of the primary and the secondary frequency scales. It was expected that the two scales might be translated with respect to each other by no more than about 1GHz. As seen in Figure 3, although they are not totally conclusive, the data strongly indicate that the two scales are indeed translated with respect to each other by no more than 0.5GHz.

∆f (MHz)

f (GHz)

V (mV)

-300 5.7 12.6 -200 5.8 11.3 -100 5.9 11.9

0 6.0 13.7 100 6.1 12.1 200 6.2 11.4 300 6.3 11.3

Table 1. Voltage output of the reference channel as a function of frequency. The first column shows the values on the frequency fine-tuning scale, while the main frequency scale showed 6GHz. The second column shows the calculated frequency and the third column shows the measured voltage output.

∆f (MHz)

f (GHz)

V (mV)

-300 6.2 12.3 -200 6.3 14.0 -100 6.4 12.2

0 6.5 11.6 100 6.6 11.5 200 6.7 12.7 300 6.8 12.0

Table 2. Voltage output of the reference channel as a function of frequency. The first column shows the values on the frequency fine-tuning scale, while the main frequency scale showed 6.5GHz. The second column shows the calculated frequency and the third column shows the measured voltage output.

Frequency scales' precision

11

12

13

14

5.5 6 6.5 7

Frequency (GHz-relative scale)

Volta

ge (m

V)

First seriesSecond series

Figure 3. Voltage output of the reference channel as a function of frequency for the first and second series of measurements (Tables 1 and 2). The lines connecting the data are drawn to guide the eye.

Next, a series of measurements was taken to study the variation of the voltage output of the oscillator with the frequency (Table 3 and Figure 4). ∆f

(MHz) f

(GHz)V

(mV) 0 10.00 10.4 -300 9.70 9.5 20 10.02 10.3 -280 9.72 9.4 40 10.04 10.0 -260 9.74 9.3 60 10.06 9.8 -240 9.76 9.4 80 10.08 9.6 -220 9.78 9.5 100 10.10 9.4 -200 9.80 9.6 120 10.12 9.2 -180 9.82 9.6 140 10.14 9.0 -160 9.84 9.7 160 10.16 8.9 -140 9.86 9.8 180 10.18 8.8 -120 9.88 10.0 200 10.20 8.7 -100 9.90 10.3 220 10.22 8.6 -80 9.92 10.4 240 10.24 8.7 -60 9.94 10.5 260 10.26 8.8 -40 9.96 10.6 280 10.28 9.0 -20 9.98 10.5 300 10.30 9.2

Table 3. Voltage output of the reference channel as a function of frequency. The first and fourth columns show the values on the frequency fine-tuning scale, while the main frequency scale showed 10GHz. The second and fifth columns show the calculated frequency and the third and sixth columns show the measured voltage output.

Frequency dependence of voltage output

8.5

9

9.5

10

10.5

11

9.7 10 10.3

Frequency (GHz-relative scale)

Volta

ge (m

V)

Figure 4. Voltage output of the reference channel as a function of frequency for the third series of measurements (Table 3). The line connecting the data is drawn to guide the eye. From Figure 4, it is obvious that the voltage output is not constant at the entire frequency spectrum; rather, it exhibits a somewhat periodic primary structure with irregular secondary components. Such a behavior is to be expected in general for any microwave circuit. The large-scale frequency behavior of the circuit can be explained by using a lumped-element approximation. In this approach, one generally finds that there are certain frequency ranges (bands) in which the circuit will exhibit very large signal loss. This model can be made more realistic by taking into consideration the finite size of the various elements of the circuit. The finite size introduces additional constraints that can be approximately described in terms of characteristic lengths, while the frequency of operation determines the local effective wavelength. Whenever the ratio of the characteristic length to the wavelength assumes certain values (usually integers or half-integers), the frequency response of the circuit exhibits a maximum or a minimum.

II) Microstrip milling After the preliminary study of the measuring devices, various techniques for constructing the antenna circuit on a standard copper-clad G-10 circuit board were investigated. The circuit board consists of a dielectric plate with a thin layer of copper on each side. The microwave circuit is made through removing some of the copper on one side of the plate. As mentioned previously, the copper that is left on that side (the circuit or upper layer) and the complete layer of copper on the other side (the ground plane or lower layer), together with the enclosed dielectric constitute a microwave propagation line architecture known as microstrip. The properties of a microstrip are not amenable to exact analytical study; however, approximate analytical results are moderately easy to derive and numerical methods can describe the properties of a microstrip with as much accuracy as required (Ref. 2). In the present work, only straight segments of microstrips are used. For this reason, milling away the copper of one layer presented itself as a very simple method of constructing the circuit. The main issue with this technique is how to remove as little of the dielectric as possible. One reason for this is that the milling cutter tends to slide on the copper surface, rather than cut through. As the pressure of the milling cutter head on the copper layer increases, it reaches a critical value and the milling cutter cuts through, removing not only the copper layer, but also some of the underlying dielectric. Another reason for the damage on the dielectric layer is that the plate is not totally flat. Moreover, clamping it in place produces enough stress to distort it even further. Furthermore, there always exists some mismatch in the alignment of the plate and the plane of horizontal motion of the milling cutter. All this deviations from planarity may cause considerable and uneven damage on the dielectric layer.

A few simple methods were used in order to avoid this damage. First, an aluminum plate on which the dielectric plate was fixed with nuts and bolts helped to minimize the bending due to clamping on the milling machine. Moreover, the milling cutter was moved in very small steps in both the horizontal and the vertical direction. Furthermore, whenever possible, the motion of the milling cutter was started on the edge of the plate in order to help the initiation of cutting through the copper layer. The direction of motion of the milling cutter with respect to the direction of its rotation was also found to play some role; however, its effect seemed to be primarily of esthetic rather than functional nature, so it was not given special attention after the first few tests. Naturally, the caution employed and the diameter of the milling cutter head used depended on the horizontal distance from the microstrip edge and the importance of the circuit. Thus, the milling of the final antenna circuit required much more time and caution and a much smaller diameter of milling cutter head than the milling of simple straight segments used in investigating methods of coupling the SMA connectors.

III) SMA connection:

Following the development of a technique for building the microstrips, two techniques for connecting a microstrip to an SMA connector were also investigated. In the first technique, the SMA connector was set normal to the surface of the circuit board. This technique however exhibited a number of difficulties in the construction and a very high signal loss, so a second technique was involved; in the latter, the SMA connector is set parallel to the circuit board, with the result of making the construction easier and reducing the signal loss substantially. In the following two subsections, the construction and performance of these two techniques are presented in detail. a) Normal-set method The first method used in order to couple the SMA connectors to the microstrip was the drilling of five holes in the plate and the placing in each of them of one of the five legs of the connector, so that the axis of the connector was normal to the plate. The holes were slightly larger than the legs, in the hope to avoid direct electrical contact between the copper layers and the legs. The four peripheral legs of connector were coupled to the ground plane layer, while the central leg of the connector was coupled to the circuit layer. The coupling was achieved by soldering the legs to the respective layers (Pictures 4, 5 and 6).

Picture 4. The normal-set method of connecting the SMA connectors to the microstrip: view of the upper layer.

Picture 5. The normal-set method of connecting the SMA connectors to the microstrip: view of the ground plane layer. Picture 6. The normal-set method of connecting the SMA connectors to the microstrip: view parallel to the dielectric plane. There were serious problems in avoiding electrical contact between the exterior legs of the connector and the upper layer, as well as between the central leg of the connector and the ground plane layer. The solder was not allowed to wet the legs in order

to avoid physical contact, resulting to high signal loss due to contact resistance. Even when there was no physical contact, the legs and the planes were so close together that an effective capacitive and inductive coupling appeared that caused the degrading of the desired coupling mode. These problems are reflected in the signal loss measurements taken for this geometry, which are listed below in Table 4 and plotted in Figure 5. V1

(mV)V2

(mV)V3

(mV)V4

(mV)44.6 21.3 8.1 3.140.5 19.3 6.9 2.935.5 16.6 6.1 2.430.4 14.1 5.0 2.025.1 11.3 3.9 1.520.1 9.1 2.9 1.115.4 7.0 2.1 0.9

Table 4. Signal loss for the normal-set method of SMA connection. The columns list the voltage output from the reference channel, the channel with an attenuator, the channel with a microstrip and the channel with an attenuator and a microstrip respectively.

Signal loss for norm al m ethod

0

5

10

15

20

25

15 20 25 30 35 40 45

Voltage in reference channel (m V)

Volta

ge in

oth

er c

hann

els

(mV)

AttenuatorMicrostripA ttenuator and microstrip

Figure 5. Signal loss in the various channels with respect to the reference channel for the normal-set method of SMA connection. Decreased slope represents increased signal loss. In this and all subsequent measurements, care was taken so that the measuring apparatus functioned in the linear regime. As mentioned earlier, the voltage output from a particular channel in this case is expected to be a constant smaller than unity times the voltage input. Thus, the signal loss for each channel can be found by fitting the voltage

output data to a linear function of the voltage output of the reference channel (which is taken to be the measuring configuration bypassing the circuit). From fitting the data to straight lines (that are not required to pass through the origin), the signal loss is found to be 3.1dB, 6.9dB and 11.0dB for the attenuator, the microstrip and the attenuator and a microstrip respectively. The small difference of 1.0dB between 11.0dB and the sum of 3.1dB and 6.9dB is attributed to the imperfect matching of the impedances of the elements of the circuit, as well as to the losses at the input and output ends of the attenuator. It is noteworthy that an estimate of the signal loss due to the microstrip propagation line itself can be performed as in Ref. 2; the result is of the order of 0.01dB/m. This means that virtually all the signal loss for the microstrip comes from its finite length as well as its connection with other components that are not matched in impedance. However, it is not straightforward to decide the relative significance of these two factors, since their effect is nonlinear and interdependent. As explained in the beginning of the section, the normal-set method for coupling the SMA connectors to the microstrip was not investigated further, because of its very poor performance, which in addition to the difficulty in isolating the legs of the connector from the copper layers is also related to the unsuitability of the geometry of the coupling to the planarity of the propagation of the microwaves along the microstrip circuit.

b) Parallel-set method In the parallel-set method, the SMA connector is placed with its axis parallel to the plane in such a way that two consecutive peripheral legs are on the one side of the plate, while the central and the remaining two peripheral legs are on the other side. Luckily, the width of the plate is such that the connector stays in place without the need for extra support. The two peripheral legs on the one side of the plate and the central leg on the other side are soldered on the corresponding copper layers. A satisfactory soldering is achieved through placing the soldering iron on the SMA connector leg, letting it heat it to a sufficient high temperature and then applying the solder on the copper layer. This is the only way found to make the solder wet the copper layer and it does not seem to significantly affect the electrical properties of the dielectric layer or the SMA connector. The signal loss measurements for this geometry are shown in Table 5 below. The signal loss in the various channels is estimated through fitting the data of Table 5 to straight lines as shown in Figures 6, 7, 8 and 9; the results of the fitting are listed in Table 6 and plotted in Figure 10.

f (GHz)

V1 (mV)

V2 (mV)

V3 (mV)

V4 (mV)

23.0 8.33 13.4 5.01 29.9 12.1 19.0 7.28 43.5 18.4 28.8 11.6

6.0

57.4 26.0 39.8 16.7 20.3 8.34 11.4 4.6 35.4 15.4 21.4 9.1 46.7 21.0 29.0 11.8

7.0

64.8 30.2 38.4 16.8 19.5 8.10 9.9 3.9 38.7 17.1 22.2 9.1 51.3 23.3 29.6 12.2

8.0

61.8 28.9 36.6 15.9 19.6 8.2 9.3 3.8 36.9 16.3 18.0 7.6 57.1 26.3 29.4 12.3

9.0

68.5 32.3 35.9 16.0 Table 5. Signal loss for the parallel-set method of SMA connection. The columns list the voltage output from the reference channel, the channel with a 3dB attenuator, the channel with a microstrip and the channel with an attenuator and a microstrip respectively, at the four frequency values of 6.0, 7.0, 8.0 and 9.0GHz.

Signal loss at 6GHz

0

10

20

30

40

50

20 30 40 50 60

Voltage in reference channel (mV)

Volta

ge in

oth

er c

hann

els

(mV)

AttenuatorMicrostripAttenuator and microstrip

Signal loss at 7GHz

0

10

20

30

40

50

20 30 40 50 60

Voltage in reference channel (mV)

Volta

ge in

oth

er c

hann

els

(mV)

AttenuatorMicrostripAttenuator and microstrip

Figure 6. Signal loss in the various channels with respect Figure 7. Signal loss in the various channels with respect to the reference channel for frequency f=6GHz. to the reference channel for frequency f=7GHz.

Signal loss at 8GHz

0

10

20

30

40

20 30 40 50 60

Voltage in reference channel (mV)

Volta

ge in

oth

er c

hann

els

(mV)

AttenuatorMicrostripAttenuator and microstrip

Signal loss at 9GHz

0

10

20

30

40

20 30 40 50 60

Voltage in reference channel (mV)

Volta

ge in

oth

er c

hann

els

(mV)

AttenuatorMicrostripAttenuator and microstrip

Figure 8. Signal loss in the various channels with respect Figure 9. Signal loss in the various channels with respect to the reference channel for frequency f=8GHz. to the reference channel for frequency f=9GHz.

f (GHz)

Attenuator signal loss (dB)

Microstrip signal loss(dB)

Attenuator and microstrip signal loss

(dB)

Discrepancy(dB)

6.0 2.94 1.18 4.71 0.58 7.0 3.08 2.15 5.66 0.42 8.0 3.10 2.03 5.55 0.43 9.0 3.08 2.63 6.10 0.39

Table 6. Signal loss in the various channels as a function of frequency. The first column shows the frequency for each data series. The second, third and fourth column show the signal loss for the attenuator, the microstrip and the combined attenuator plus microstrip channel with respect to the reference channel. The fifth column lists the difference between the entry in the fourth column and the sum of the entries in the second and third column.

Frequency dependence of signal loss

0

0.5

1

1.5

2

2.5

3

3.5

6 7 8 9

Frequency (GHz)

Sign

al lo

ss (d

B)

AttenuatorMicrostripD iscrepancy

Figure 10. Frequency dependence of the signal loss in the various channels with respect to the reference channel. The curves are drawn to guide the eye. It is apparent from Figure 10 that the attenuator signal loss depends very weakly on the frequency, while the microstrip signal loss depends more strongly and non-monotonically on the frequency. Still, the signal loss is smaller than 3dB for the entire frequency range 6-9GHz. For that reason, the parallel method of coupling the SMA connector to the microstrip is the technique used in all the subsequent investigations. Also, experience in the milling of the microstrip and the soldering of the connector contributed to decrease the signal loss even further.

IV) Microstrip coupling: In order to couple two microstrips together, two methods were investigated. In the

first method, the two microstrips belong to two different circuit boards that are laid back to back, so that they share a common ground plane. This configuration was investigated in the hope that the perturbations in the antenna operation would be minimal, since the receiver would be fairly isolated from the rest of the antenna circuit through the ground plane. However, this particular configuration proved to have a high signal loss and to impose design constraints that necessitated a complicated construction procedure. For that reason, a second method of coupling two microstrips was developed, in which the two microstrips belong in the same circuit board. This second method proved to be satisfactory with regard to signal loss and allowed for a relatively simple construction. In the following two subsection, each of the two coupling method is presented in detail.

However, it should be noted at this point, that since the receiver is composed of four microstrips set in a very special configuration, any technique used is required to introduce only small perturbations in the structure during the measurement of the currents at the four midpoints. It is clear that the design used should be characterized by a four-fold symmetry axis around the center of the antenna. Moreover, it seems reasonable that a T-junction design, in which two microstrips touch normal to each other, will perturb significantly the configuration of currents of the antenna, since the microstrip normal to a receiver microstrip might function as an extension of the receiver. a) Hole coupling method

As mentioned previously, the first technique for the coupling of two microstrips

that was investigated consists of placing two plates together so that their ground planes are in contact. A fine wire passes through a narrow hole in each of the two plates and couples microstrips situated on their upper layers. The one hole was drilled very close, but not inside the one microstrip and the other hole was situated at the end of the other microstrip. Two views of a device constructed to test the hole coupling method are shown below (Pictures 7 and 8).

G

F

E

DC

B

A

Picture 7. View of a device using the hole coupling method. The two dielectric plates (A, B) are pressed tightly together. The signal enters through SMA connector C and exits through SMA connectors D (straight channel) and E (coupled channel). The fine wire is soldered at point F on the straight channel microstrip and goes through a hole at G to connect to the coupled channel microstrip.

G

F

E

DC

B

A

Picture 7. Alternate view of a device using the hole coupling method. The dielectric plate A (B) containing the straight channel (coupled channel) microstrip is the lower (upper) one. The signal enters through SMA connector C and exits through SMA connectors D (straight channel) and E (coupled channel – not shown clearly in the picture). The fine wire, whose one end is soldered at some point on the straight channel microstrip, goes through a hole at F to connect to the coupled channel microstrip at point G.

The measurements of the signal loss with respect to the reference channel for two

frequencies are listed below in Table 7 and are plotted in Figures 11 and 12.

V1 (mV)

V1' (mV)

V2 (mV)

V2' (mV)

V3 (mV)

V3' (mV)

21.5 7.9 11.8 4.4 1.07 0.039 46.8 20.4 29.2 12.0 2.84 1.04 65.7 30.5 42.7 18.6 4.22 1.65 f

=6G

Hz

97.0 47.4 63.2 29.2 7.04 2.73 V1

(mV)V1'

(mV)V2

(mV)V2'

(mV)V3

(mV)V3'

(mV) 50.1 22.5 29.3 12.2 0.048 0.019

f=8G

Hz

92.8 44.8 56.9 25.5 0.061 0.027 Table 7. Signal loss for hole method of microstrip coupling. The first, third and fifth columns show the voltage output from the reference channel, the single microstrip channel and the coupled microstrip channel respectively, at the two frequency values of 6.0 and 8.0GHz. The second, fourth and sixth columns show the voltage output from the reference channel with an attenuator, the single microstrip channel with an attenuator and the coupled microstrip channel with an attenuator respectively, at the same two frequency values of 6.0 and 8.0GHz.

Signal loss at f=6GHz

0

10

20

30

40

50

60

70

20 40 60 80 100

Voltage in reference channel (mV)

Figure 11. Signal loss in the various channels with respect to the reference channel for frequency f=6GHz.

Signal loss at f=8GHz

0

10

20

30

40

50

60

50 60 70 80 90 100

Voltage in reference channel (mV)

Figure 12. Signal loss in the various channels with respect to the reference channel for frequency f=8GHz. From fitting the data to straight lines, it is found that the signal loss for the reference, the single microstrip and the coupled microstrip channels without (with) an attenuator is 2.8dB, 1.7dB (4.8dB) and 11.0dB (14.5dB) for f=6GHz and 2.8dB, 1.9dB (5.1dB) and 35.2dB (37.0dB) for f=8GHz. The signal losses for the attenuator and the same microstrip are consistent with the previous measurements. Moreover, it is clear that the coupled microstrip signal loss depends strongly on the frequency. In order to investigate this dependence, the following three series of measurements were taken (Table 8 – Figures 13 and 14).

f (GHz)

V2 (mV)

f (GHz)

V2 (mV)

f (GHz)

V2 (mV)

6.0 2.89 5.7 3.88 5.90 3.55 6.5 1.47 5.8 2.65 5.92 3.85 7.0 0.38 5.9 3.46 5.94 4.05 7.5 0.107 6.0 3.05 5.96 3.85 8.0 0.047 6.1 2.29 5.98 3.45 8.5 0.065 6.2 1.60 6.00 3.15 9.0 0.103 6.3 0.72 6.02 2.80 9.5 0.084 6.04 2.55 10.0 0.089 6.06 2.45 10.5 0.085 6.08 2.35

6.10 2.35 Table 8. Signal loss in the hole coupling method. The first, third and fifth columns show the frequency values sampled at the three frequency ranges 6-10.5GHz, 5.7-6.3Ghz and 5.9-6.1Ghz respectively. The second, fourth and sixth columns show the voltage output of the coupled microstrip at these frequency values.

Signal loss frequency dependence

0

0,5

1

1,5

2

2,5

3

3,5

6000 6500 7000 7500 8000 8500 9000 9500 10000 10500 11000

Frequency (MHz)

Volta

ge in

cou

pled

str

iplin

e (m

V)

First series

Figure 13. Signal loss of the coupled microstrip with respect to frequency for the frequency range 6-0.5GHz. The curve is drawn to guide the eye.

.3GHz and 5.9-6.1GHz. The curves are drawn to guide the eye.

1

Signal loss frequency dependence

Figure 14. Signal loss of the coupled microstrip with respect to frequency for the frequency ranges 5.7-

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5700 5800 5900 6000 6100 6200 6300

Frequency (MHz)

Volta

ge in

cou

pled

str

iplin

e (m

V)

Second seriesThird series

6

From the figures it becomes apparent that the signal loss of the coupled microstrip xhibits frequency dependence in many scales. In the large scale (Figure 13), the signal e

loss increases fast with frequency in the range f

b) Bridge method The high signal loss and the low-pass filter structure of the frequency dependence as well as technical difficulties in its construction make the hole coupling method very unsatisfactory, so a second technique of coupling the microstrips was investigated. In this method, the two microstrips are milled on the same circuit board and have a common ground plane. The end of one microstrip is placed at some distance from the midpoint of the other microstrip. It is very hard to estimate the optimal distance: if it is too small, the perturbation on the current distribution will be important; if it is too large, the coupling of the two microstrips will be very weak. In order to intensify the coupling, the end of the one microstrip and the midpoint of the other are connected by a fine wire. In principle, one can choose the distance of the two microstrips and the shape of the ending section such as to achieve matched impedances and minimal perturbations. This optimization was not pursued, because the main objective was to explore different techniques rather than develop the optimal one. Moreover, the optimization would require the use of numerical analysis and the resulting profile design would presumably be hard to manufacture in a milling machine. For that reason, a simple rectangular profile was used for the microstrips. A view of the upper layer of a device coupling two microstrips through the bridge method is shown in Picture 9.

F E

D

C

B

A

Picture 9. Coupling of two microstrips through the bridge method. The entire circuit is contained in one circuit board A. The signal enters through SMA connector B and exits through SMA connectors C (straight channel) and D (coupled channel). The fine wire is soldered at points E and F on the straight and coupled channel microstrips respectively.

The measurements of signal loss taken for the bridge method are listed in Table 9 and are plotted in Figures 15 and 16.

V0 (mV)

V1 (mV)

V2 (mV)

21.2 13.8 3.1 50.9 36.2 8.8 61.7 42.7 11.2 f

=6G

Hz

74.9 52.2 14.6 V0

(mV)V1

(mV)V2

(mV)22.1 7.8 1.7 38.2 15.2 3.5 57.3 22.5 5.4 f=

12G

Hz

71.8 30.0 7.2 Table 9. Signal loss for the bridge coupling method. The first, second and third columns show the voltage output from the reference, the single microstrip and the coupled microstrip channel respectively, for the frequency values of 6 and 12GHz.

Signal loss for f=6GHz

0

10

20

30

40

50

60

20 40 60 80

Voltage in reference channel (mV)

Figure 15. Signal loss in the various channels with respect to the reference channel for frequency f=6GHz.

Signal loss for f=12GHz

0

5

10

15

20

25

30

35

20 40 60 80

Voltage in reference channel (mV)

Figure 16. Signal loss in the various channels with respect to the reference channel for frequency f=12GHz. Fitting the data to straight lines, the signal loss is found to be 1.5dB (3.6dB) in the same microstrip and 6.8dB (9.6dB) in the coupled microstrip channel for frequency of f=6GHz (f=12GHz). The frequency dependence of the signal loss in the coupled microstrip was investigated further by taking the measurements listed in Table 10 and plotted in Figure 17. From Figure 17 it is easy to see that the data for the reference channel exhibit a periodicity in the frequency dependence. The frequency dependence of the coupled microstrip has an irregular form that exhibits high signal loss in the range 6.5-8.5GHz and low signal loss for frequencies f

f (GHz)

V1 (mV)

V2 (mV)

6.0 76.4 14.4 6.5 68.6 9.1 7.0 74.1 2.3 7.5 64.5 0.27 8.0 72.0 1.0 8.5 62.1 3.53 9.0 72.6 4.3 9.5 69.8 4.3

10.0 76.6 7.6 10.5 65.1 9.9 11.0 74.2 11.5 11.5 68.6 8.5 12.0 74.9 7.6

Table 10. Signal loss for the bridge method of coupling microstrips. The first column lists the values of the frequency and the second and third columns show the voltage output in the reference and in the coupled microstrip channel.

Signal loss frequency dependence

0

0,2

0,4

0,6

0,8

1

1,2

6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12

Frequency (GHz)

Nor

mal

ized

vol

tage

in v

ario

us c

hann

els

(mV) Reference channel

Coupled channel

Figure 17. Signal loss in the reference and in the coupled microstrip channel as a function of frequency. The data have been normalized by dividing with the maximum value in the frequency interval.

V) Final setup: a) Antenna The techniques described in the previous sections were used to build the antenna circuit (Picture 10).

E D

C

BA

Picture 10. The antenna circuit. It is mainly comprised of the four microstrips (A) constituting the actual receiver and the four microstrips (B) connecting the receiver to the SMA connectors (C). The three attenuators (D) and the SMA cable (E) are also visible.

The receiver is consisting of four microstrips that are built according to the design in Figure 2. The midpoints of the each receiver microstrip are connected to another microstrip that ends at the edge of the dielectric plate using the bridge method. Each of these terminal microstrips is connected to an SMA connector through the parallel method. During the testing process that will be described in the following section, the signal output of one of the SMA connectors was measured while the three remaining SMA connectors were terminated using a 20dB attenuator for each, as shown in Picture 10. It should be noted that considerable attention was paid in building the circuit in a symmetric fashion. For that reason, the size of the welding spots was kept as small as possible and the antenna circuit was given a square shape. Moreover, the fine wires used to connect the receiver and the terminal microstrips were welded in pairs and then the excess wire was removed with a cutter. The small total area of the antenna circuit is due to the size constraints of the milling machine holder. In principle, it should be possible to use a custom-made holder for the antenna circuit that would allow the antenna square to be larger in size. This could presumably decrease the perturbations in the receiver function due to the existence of the SMA connectors and the edge of the dielectric. However, the antenna circuit constructed showed no significant signs of problems attributable to the small size of the antenna circuit, so the utility of building a larger circuit was questionable.

b) Support rack In order to test the antenna circuit, it was mounted in the support rack shown in Picture 11.

F

E

D

CBA

Picture 11. The support rack for testing the antenna circuit. The antenna circuit (A) is glued on a cylinder (B) that is allowed to rotate around an axis (C) on its base (D). The horn (E) and the antenna support are set on a long piece of microwave absorbent material (F) in a way that permits the change of their distance. The antenna circuit is glued on a plastic cylinder whose axis is made to pass through the center of the circuit. The diameter of the cylinder is about half the length of the edge of the antenna circuit, so that the cylinder is protected from the incident microwave beam by the ground plane layer, resulting in decreased back-scattering. The cylinder is drilled and tapped on the other end and a screw is used to support it in a way that allows it to rotate around its axis. The head of the screw is used as a pivot to roughly measure the angle of rotation of the cylinder around its axis in multiples of 30°. This measuring apparatus is certainly of small precision, but it amply suffices for the scope of the testing processes in this experimental project. The horn that was used produces a polarized microwave beam. Together with the antenna support, it is mounted on a long piece of microwave absorbent material in a way that allows changing their respective distance, which is measured horizontally from the horn diode to the surface of the antenna circuit.

D. Measurements: Following the construction of the antenna circuit and the setting up of the measuring apparatus, the polarization, beam and band characteristics of the antenna were investigated. The most important property is certainly the polarization sensitivity of the antenna. This can be precisely quantified by the use of a number of parameters; from a physical point of view, the two most important features are a square-sinusoidal angle dependence of the voltage output and a large maximum-minimum voltage output ratio. The first measures the linearity of the antenna response in the incoming signal and the second measures the decoupling between the two polarization channels. The constructed antenna circuit has been seen to exhibit both features in a satisfying degree. The second property of interest is the beam characteristics of the antenna circuit that can be defined as the properties of the resulting beam, if one uses the antenna as a transmitter rather than a receiver. The rough nature of the measuring apparatus does not allow a precise investigation; nevertheless, the measurements are consistent with a wide beam profile. The last characteristic that is investigated is the frequency dependence of the voltage output of the antenna. Due to the fact that the voltage output of the oscillator also depends on the frequency, it is not straightforward to determine the detailed frequency response of the antenna. However, it is possible to identify the large-scale band structure, which exhibits a peak around 11GHz. The investigation of the above properties is described with more details in the following subsections. I) Angle dependence – polarization characteristics Using the experimental setup that is described in the previous section, the following series of measurements of the signal output were taken for the four SMA connectors (Table 11 and Figure 18) at the frequency of 10GHz and the distance of 13cm.

θ (°)

V1 (mV)

V2 (mV)

V3 (mV)

V4 (mV)

0 3.3 2.1 1.96 2.30 30 2.2 1.58 0.96 1.40 60 0.90 0.98 0.24 0.63 90 0.07 0.15 0.05 0.04

120 0.62 0.53 0.68 0.88 150 1.72 1.36 1.60 2.2 180 2.7 1.87 1.95 2.4 210 1.98 1.50 1.10 1.20 240 0.85 0.74 0.31 0.35 270 0.04 0.06 0.05 0.06 300 0.94 0.59 1.05 1.13 330 2.0 1.49 1.65 2.00

Table 11. The voltage output from the antenna as a function of angle. The first column shows the angle of the terminal microstrip with the polarization plane of the incident microwave beam. The second, third, fourth and fifth column list the voltage output of the first, second, third and fourth SMA connector respectively.

Figure 18. The angle dependence of the signal output of the four SMA connectors. The interpolation lines come from fitting the experimental data that have been normalized with respect to the maximum value. From Figure 18, it is obvious that the data obey a square-sinusoidal law of the following form:

}cos)]cos(21[cossin2)]1(cos)1(cos[(

sin)]cos(2{[

222

22

2220

θχϕαββα

θθαχββϕα

θχϕαββα

+++

++++

+−++=VV where V0, α, β, ϕ and χ are parameters that describe the polarization characteristics of the incident microwave beam and the angle response of the receiver. The imperfections of the fit are mainly due to the imperfect alignment of the horn with the antenna circuit axis and to the reflections of the microwave beam on the supporting structure and the environment, as well as due to the imprecision of angle measurement. The imperfect way of terminating the three SMA connectors whose voltage output is not measured at a given moment can also act as a source of perturbations. Still, it follows from Figure 18 that the antenna exhibits a high maximum-minimum voltage output ratio, which signifies a strong decoupling between the two polarization modes.

II) Distance dependence – beam characteristics Two more series of measurements were taken in order to investigate the dependence of the signal output on the distance between the horn and the antenna circuit (Table 12 and Figure 19); in order to investigate the distance dependence of the voltage output, the voltage input to the horn was kept constant to that of the previous series of measurements.

θ (°)

V1’ (mV)

V1’’ (mV)

0 12.6 1.29 30 11.9 0.96 60 5.07 0.40 90 0.01 0.02

120 8.1 0.42 150 13.0 0.93 180 12.3 1.13 210 12.3 0.69 240 4.65 0.16 270 0.02 0.02 300 6.40 0.55 330 11.4 1.00

Table 12. The voltage output from the first SMA connector for two different distances. The first column shows the angle of the terminal microstrip of the first SMA connector with the polarization plane of the incident microwave beam. The second and third columns list the voltage output at distances of 3.5cm and 22.5cm respectively. From Figure 19 it is obvious that in all three distances the angle dependence of the voltage output from the first SMA connector exhibits the general structure predicted by a square-sinusoidal law. The deviations seem more pronounced in the series of measurements taken at the shortest distance. One reason for that is presumably the greatest importance of axis misalignment in this case; however, these deviations are also consisted with the expectation of a Gaussian broad beam profile for the antenna, since, at the shortest distance, the beam originating on the horn is expected to cover the receiver only partially. Moreover, the peak values of the (un-normalized) voltage output exhibit a decrease with distance as shown in Figure 20.

Polarization distance dependence

0

0,2

0,4

0,6

0,8

1

0 30 60 90 120 150 180 210 240 270 300 330 360

Angle (degrees)

Nor

mal

ized

vol

tage

Short distanceMedium distanceLarge distance

Figure 19. The angle dependence of the voltage output from the first SMA connector for three different distances (3.5cm, 13cm and 22.5cm). The experimental data have been normalized with respect to the maximum value.

Peak voltage output distance dependence

0,01

0,1

1

10

100

1000

1 10 100

Distance (cm)

Peak

vol

tage

out

put (

mV)

Data seriesSquare law fitBest power law fit

Figure 20. The dependence of the peak voltage output of the first SMA connector on the distance between the horn and the antenna circuit. The square law fit is performed on the two right-most points, while the best power law fit is performed on all three points. The best power law fit on all data points results in an negative exponent of 1.24. This value differs from the value of 2 expected for a spherical microwave beam; the discrepancy is attributed to the fact that the beam cannot be described as spherical in the very small distance region. If the fit is performed instead on the two data points

corresponding to the medium and long distance region, an inverse law appears to be in close agreement with the observed behavior. This fact is consistent with a wide beam profile for the antenna; nevertheless, attention should be once again drawn to the large error bars inherent in the measurement of the distance and the actual peak values, due to the rough nature of the support rack.

II) Frequency dependence – band characteristics Finally, in order to investigate the dependence of the voltage output of the antenna circuit on the frequency of the incident microwave beam, the following series of measurements was taken (Table 13 and Figure 21).

F (GHz)

V1 (mV) 9.2 0.318

6.0 0.0079 9.4 0.40 6.2 0.0070 9.6 0.57 6.4 0.0105 9.8 0.55 6.6 0.0115 10.0 0.62 6.8 0.0188 10.2 0.68 7.0 0.0280 10.4 0.71 7.2 0.0488 10.6 0.64 7.4 0.0890 10.8 0.68 7.6 0.192 11.0 0.86 7.8 0.217 11.2 0.71 8.0 0.207 11.4 0.38 8.2 0.182 11.6 0.29 8.4 0.179 11.8 0.25 8.6 0.159 12.0 0.26 8.8 0.277 12.2 0.32 9.0 0.279 12.4 0.25

Table 13. The frequency dependence of the voltage output of the first SMA connector. The first and third columns show the frequency. The second and fourth columns show the corresponding value of the voltage output.

Signal gain frequency dependence

0

0,2

0,4

0,6

0,8

1

6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5

Frequency (GHz)

Volta

ge (m

V)

Figure 21. The frequency dependence of the voltage output of the first SMA connector.

From Figure 21 it is seen that the antenna frequency dependence is not monotonic

and exhibits peaks and troughs. According to the raw data, the best reception occurs for the frequency value of about 11GHz, while the reception is better than 50% of the maximum value for the frequency range of 9.5-11.5GHz. As cautioned earlier, it is not clear how to determine the detailed frequency response of the antenna, since the voltage output of the oscillator is also frequency dependent. Nevertheless, the large-scale structure of the antenna frequency response is apparently not substantially different from that shown in Figure 21.

D. Conclusion In the present project, the physical principles concerning the construction of a planar polarization-sensitive microwave antenna were investigated. Emphasis was given in the development of various techniques for each stage of the construction process. From the experimental measurements, it follows that the use of comparatively simple profiles for the microstrips in conjunction with planar coupling methods ensures a satisfying signal reception and good polarization characteristics. Specifically, it was found that coupling methods based on the principle of using a single propagation plane are superior to other methods that make use of multiple propagation planes or normal propagation lines. Furthermore, it was found possible to construct the antenna circuit in a manner symmetric enough to allow for high polarization sensitivity, both in the sense of obeying a square-sinusoidal law and exhibiting a high maximum-minimum ratio. Finally, the frequency response of the antenna is not uniform; still the antenna behaves in a satisfying way for frequencies around 10GHz. Concluding, it is important to note that, although there was no attempt to optimize the antenna design or manufacturing processes, the resulting antenna circuit operated in a very satisfying manner as a polarization-sensitive receiver, fulfilling the experimental project’s goal.

E. References

1. Goutam Chattopadhyay, Dual Polarized and Balanced Receivers at Millimeter and Submillimeter Wavelengths, Ph. D. Thesis, California Institute of Technology, 2000

2. Pozar, David M., Microwave Engineering, John Wiley, Second Edition, 1998 3. E. M. Leitch, C. Pryke, N. W. Halverson, J. Kovac, G. Davidson, S. LaRoque, E.

Schartman1, J. Yamasaki, J. E. Carlstrom, W. L. Holzapfel, M. Dragovan, J. K. Cartwright, B. S. Mason, S. Padin, T. J. Pearson, A. C. S. Readhead, M. C. Shepherd, Experiment Design and First Season Observations with the Degree Angular Scale Interferometer, Astroph. J. 568, 28

Student’s name:Vassilios PapathanakosPhysics Department, Princeton UniversityOctober 2002�Table of contents:

A. IntroductionB. Design of the Antenna

(f(MHz)V(f(MHz)V(fII) Microstrip millingIII) SMA connection:a) Normal-set methodIV) Microstrip coupling:However, it should be noted at this point, that since the receiver is composed of four microstrips set in a very special configuration, any technique used is required to introduce only small perturbations in the structure during the measurement of the cua) Hole coupling method

(mV)V2(mV)V0V) Final setup:a) AntennaD. Measurements:I\) Angle dependence – polarization characterist

D. ConclusionE. References