Fabrication Processes for RF and Microwave Circuits
3.6 Characterization of Materials for RF and Microwave Circuits
3.6.2 Measurement of Planar Line Properties
3.6.2.2 Non-resonant Lines
The measurement techniques described in the previous sections can provide high measurement accuracy primarily because they make use of resonant circuits in one form or another. These circuits utilize voltage magnification, which increases the sensitivity of the measured parameters. A much simpler technique is to make use of non-resonant lines of different lengths.
Whilst this will not have same degree of accuracy as the more complex resonant structures, with modern measurement instrumentation it can provide useful information on the properties of planar lines. Also, using non-resonant lines enables swept measurements over a continuous range of frequencies to be obtained, whereas resonant structures can only provide data at a number of discrete frequencies. The basic non-resonant circuit configuration is shown in Figure 3.32, and consists of two microstrip lines of equal width, but unequal length.
The meandered line shown in Figure 3.32 simply provides an additional path length compared to the straight through line. The spacing between the meandered sections must be large enough to avoid edge coupling, and the corners should be chamfered to minimize the corner discontinuity. If the same voltage,V1, is applied to each line the loss per unit length of
V1
V1
V2S
V2M
Figure 3.32 Non-resonant test circuit.
k k 𝛼= |V2M|−|V2S|
ΔL , (3.46)
whereΔLis the difference in length between the two lines. Similarly, the phase change per unit length at a given frequency is given by
𝜙=∠(V2M) − ∠(V2S)
ΔL . (3.47)
The substrate wavelength and effective relative permittivity can then be found from 𝜙=2𝜋
𝜆s
=2𝜋 𝜆o
√𝜀MSTRIPr,eff , (3.48)
where𝜆ois the free-space wavelength at the measurement frequency.
The use of the non-resonant line technique assumes that the measurement conditions are the same for both the straight line and the meandered line, and in particular that the characteristics of the launchers are identical. For microstrip lines a high degree of launcher repeatability is possible by mounting the test circuit in a ‘Universal Test Fixture’ as shown in Figure 3.33a. With this type of fixture the test circuit is clamped between two sprung jaws, one of which is fixed in position and the other movable in thex−yplane through the use of sliders. RF signals are connected to the jig through miniature coaxial connectors and contact made through the use of flat tabs, which can be precisely positioned over the ends of the microstrip lines. Repeatability of circuit mounting with this type of jig is extremely good, typically being better than±0.1 dB up to 20 GHz, with phase repeatability better than±1∘.
Non-resonant lines with a CPW format can also be used for testing at higher millimetre-wave frequencies, with the test circuit mounted in a conventional probe station as shown in Figure 3.33b.
It should also be noted that when designing CPW lines with a finite ground plane, correct choice of the widths of the ground strips is important in minimizing line losses. The cross-section of a FGCPW line is shown in Figure 3.34.
Ghione and Goano [43] showed that the following relationship must be satisfied if the influence of the finite ground on line loss is to be negligible (<10% of the ideal case ofc= ∞).
c>2b. (3.49)
The use of the swept frequency technique can also provide informative displays showing the significance of the various sources of loss as a function of frequency.
(a) (b)
Figure 3.33 Mounting of planar test circuits: (a) microstrip test circuit mounted in a universal test fixture and (b) CPW test circuit mounted on a conventional probe station.
c b
Figure 3.34 Cross-section of a symmetrical FGCPW line.
k k
3.6 Characterization of Materials for RF and Microwave Circuits 119
Example 3.13 The total line loss in dB/mm obtained from a broadband sweep of a 50Ωmicrostrip line is shown in Figure 3.35.
The line data are: Substrate: Relative permittivity=9.8 Thickness=0.25 mm Conductor: Copper (𝜎=5.87×107S/m)
RMS surface roughness=370 nm
0 0.05 0.1 0.15 0.2 0.25
10 20 30 40 50
Frequency (GHz)
Loss (dB/mm)
Figure 3.35 Microstrip line loss.
Neglecting radiation loss, determine:
(i) The loss tangent of the dielectric at 10, 30, and 50 GHz
(ii) The percentage contributions of bulk conductor loss, conductor surface loss, and dielectric loss at 10, 30, and 50 GHz, and show the results graphically. Comment upon the results.
Solution
(i) Using microstrip graphs:
50Ω ⇒ w
h =0.9 ⇒ w=0.9×0.25 mm=0.225 mm.
w
h =0.9 ⇒ 𝜀MSTRIPr,eff =6.6.
10 GHz:𝜆o= c
f = 3×108
10×109 m=30 mm 𝜆s= 30
√6.6
mm=11.68 mm.
30 GHz:𝜆o= c
f = 3×108
30×109 m=10 mm 𝜆s= 10
√6.6
mm=3.89 mm.
50 GHz:𝜆o= c
f = 3×108
50×109 m=6 mm 𝜆s= 6
√6.6
mm=2.34 mm.
Calculating the skin depth:𝛿s=(𝜋𝜇of𝜎)−0.5
𝛿s(10 GHz) = (𝜋×4𝜋×10−7×1010×5.87×107)−0.5m=0.66μm, 𝛿s(30 GHz) =0.38μm,
𝛿s(50 GHz) =0.30μm.
Reading total loss from graph:𝛼t=0.038 dB/mm at 10 GHz, 𝛼t=0.130 dB/mm at 30 GHz, 𝛼t=0.246 dB/mm at 50 GHz.
Now𝛼t=𝛼d+𝛼c,
(Continued)
k k where
𝛼d=dielectric loss
𝛼c=total conductor loss (sum of bulk and surface loss).
The value of𝛼cat the three frequencies being considered can be found through substitution in Eq. (3.8):
𝛼c(10 GHz) = 0.072×√ 10 0.225×50
( 1+32
𝜋tan−1
[0.24×0.3702 0.662
])
dB∕mm
=0.035 dB∕mm.
Similarly,
𝛼c(30 GHz) =0.117 dB∕mm, 𝛼c(50 GHz) =0.207 dB∕mm.
The dielectric loss can now be found by subtracting the calculated conductor loss from the total loss read from the swept frequency response:
𝛼d(10 GHz) =𝛼t(10 GHz) −𝛼c(10 GHz) = (0.038−0.035)dB∕mm=0.003 dB∕mm, 𝛼d(30 GHz) =𝛼t(30 GHz) −𝛼c(30 GHz) = (0.130−0.117)dB∕mm=0.013 dB∕mm, 𝛼d(50 GHz) =𝛼t(50 GHz) −𝛼c(50 GHz) = (0.246−0.207)dB∕mm=0.039 dB∕mm.
Using Eq. (3.6):
10 GHz: 0.003=27.3×9.8× (6.6−1) ×tan𝛿 6.6× (9.8−1) × 1
11.68 ⇒ tan𝛿=0.0014, 30 GHz: 0.013=27.3×9.8× (6.6−1) ×tan𝛿
6.6× (9.8−1) × 1
3.89 ⇒ tan𝛿=0.0020, 50 GHz: 0.039=27.3×9.8× (6.6−1) ×tan𝛿
6.6× (9.8−1) × 1
2.34 ⇒ tan𝛿=0.0035.
(ii) We can find the bulk conductor loss by puttingΔ =0 in Eq. (3.8) giving:
𝛼c,bulk(10 GHz) = 0.072×√ 10
0.225×50 dB∕mm=0.020 dB∕mm, 𝛼c,bulk(30 GHz) = 0.072×√
30
0.225×50 dB∕mm=0.035 dB∕mm, 𝛼c,bulk(50 GHz) = 0.072×√
50
0.225×50 dB∕mm=0.045 dB∕mm.
The surface loss is given by𝛼c,surface=𝛼c−𝛼c,bulk, i.e.
𝛼c,surface(10 GHz) = (0.035−0.020)dB∕mm=0.015 dB∕mm, 𝛼c,surface(30 GHz) = (0.117−0.035)dB∕mm=0.082 dB∕mm, 𝛼c,surface(50 GHz) = (0.207−0.045)dB∕mm=0.162 dB∕mm.
Summary:
f (GHz)
𝜶t
(dB/mm)
𝜶d
(dB/mm)
𝜶c,bulk
(dB/mm)
𝜶c,surface
(dB/mm)
10 0.038 0.003≡7.9% 0.020≡52.6% 0.015≡39.5%
30 0.130 0.013≡10.0% 0.035≡26.9% 0.082≡63.1%
50 0.246 0.039≡15.9% 0.045≡18.2% 0.162≡65.9%
k k
3.6 Characterization of Materials for RF and Microwave Circuits 121
Just for illustrative purposes the data presented in the table can also be shown using Pie-charts, as in Figure 3.36.
Comment: As the frequency increases the losses due to the dielectric, and particularly those due to the roughness of the conductor surface, assume much greater importance.
It is also useful to add the calculated conductor losses to the swept frequency response to emphasize the relative significance of the sources of loss, as shown in Figure 3.37.
Dielectric Conductor
surface
Bulk conductor
10 GHz 30 GHz 50 GHz
Figure 3.36 Constituent components of line loss.
0 0.05
0.1 0.15 0.2 0.25
10 20 30 40 50
Loss (dB/mm)
Frequency (GHz)
αc αc,bulk
Dielectric loss
Conductor surface loss
Conductor bulk loss αt
Figure 3.37 Influence of various sources of line loss.