A quarter-wave transformer is a simple impedance transformer which is commonly used in impedance matching in order to minimize the energy which is reflected when a transmission line is connected to a load. The quarter-wave transformer uses a transmission line with different characteristic impedance and with a length of one-quarter of the guided-wavelength to match a line to a load.
A basic schematic is shown in Fig. 1.
From the literature [1] we write the equation that determines the value of the impedance
From this impedance, the width of the microstrip can be calculated by a more complex equation [1].
The guided wavelength λ is shorter than the free-space wavelength due to the presence of the dielectric substrate. The equation for guided wavelength is also given in [1].
The quarter-wave transformer in this example connects a 50 Ω line to a 100 Ω load at 1 GHz, and is realized using a microstrip technology on an FR-4 substrate and modeled in CST Studio Suite® as shown in Fig 2.
This model has a microstrip of 50 Ω that needs to be matched to a load of 100 Ω. By using Eq. 1 we find that the transforming line has 70.71 Ω. The microstrips must be realized on a substrate with
Parameter | Value | Description |
---|---|---|
h | 1.2 mm | Substrate thickness |
t | 0.035 mm | Metallization thickness |
eps r | 4.3 | Substrate permittivity |
Z0 | 50 Ω | System characteristic impedance |
RL | 100 Ω | Load impedance |
W50 | 2.35 mm | 50 Ω line width |
W70 | 1.23 mm | 70.71 Ω line width |
I70 | 41.84 mm | Transformer length |
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Fig. 3 shows the E-field phase animation. On that animation we can see that at the resonant operating frequency (1 GHz) there is no reflection from the load, and therefore the load of 100 Ω is matched to the input line of 50 Ω. In Fig. 8 we plot the broadband frequency response of the transformer. Because there is a 10 mm microstrip leading up to the transformer, the S-Parameters need to be de-embedded. This is done using “De-embed S-Parameter” under the “S-Parameter Calculations” menu on the “Post Processing” ribbon, with a distance to reference plane of -10 mm.
Note that the return is at a minimum at frequencies where the
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