Introduction
What are directional couplers? Directional couplers are coupled two waveguides as schematically shown in Figure 8.1 It may be designed as forward only (uni-directional) or in forward and backward directions (bi-directional). When used with co-planar waveguides (CPW) they may be fabricated as a staircase; one on top of each other. The assembly may be used to transmit signals in quantum formats from one qubit to another. The latter requires cooling of the CPWs to almost zero temperature.
Conventional coplanar waveguides (CPWs) consist of a single conducting track printed onto a dielectric substrate, together with a pair of return conductors, one to either side of the track (loosely referred to as ground) as shown in Figure 8.1 of the CPW lab. All three conductors are on the same side of the substrate, and hence are coplanar. The return conductors are separated from the central track by a small gap, G, with a given width along the length of the line. Away from the central conductor, the return conductors usually extend to large distances.
The electromagnetic wave carried by a coplanar waveguide exists partly in the dielectric substrate, and partly in the air above it. In general, the dielectric constant of the substrate will be different (and greater) than that of the air, so that the wave is travelling in an inhomogeneous medium. In consequence CPW will not support a true TEM wave; at non-zero frequencies, both the E and H fields will have longitudinal components (a hybrid mode). However, these longitudinal components are usually small and the mode is better described as quasi-TEM (see for example, a text book by Pozar).
Pre-Lab
- What is the importance of planar devices?
- What are the pro and con of planar elements?
- Are the CPW modes a true TEM?
- Compare the CPW modes to micro-strip modes
Materials
- Copper Mountain Technologies VNA (804U)
- University Kit Hardware (N-SMA cables, Band Pass Filter, Wi-Fi Antenna, Torque Wrenches (N and SMA), 2 SMA-SMA adapters, Calibration Kit N911/912).
Lab objectives
To assess the coupling between two adjacent CPW waveguides, one on top of each other.
General Best Practices
Before starting this lab, there are few practices one should keep in mind. They are as follows:
- It is always a good practice to warm up the VNA before using it to get accurate measurements.
- Second important thing is to check if the cables are in a good condition. A quick way to do this is to connect the cable end to Short, Open and Load and see the corresponding S11 graph in Log Magnitude.
- Both the open and short connections must yield a flat line very close to 0 dB. The load connection must give you a very low return loss (around -40 dB).
- Always make sure to use a torque wrench while making the connections.
- Also make sure that the VNA is in an ESD (Electrostatic Discharge) safe environment and the operator is wearing an ESD wrist wrap.
- With these prechecks performed, you can now go ahead and make the measurements.
General Full 2-Port Calibration Procedure for CMT804U (Link to this complete calibration procedure video). Also see previous labs for a 2-port VNA calibration procedure.
Lab Procedure
- Design a CPW on a PCB board supplied. Consider the central lead width, W, based on the gap between the SMA connector's 'legs' (also supplied)
- Simulate your design using COMSOL, HFFS, Microwave Studios and the like.
The final product of a single CPW may look like this:
- Fabricate two lines across the PCB board using facilities available at the NJIT Maker Space.
- Characterize your CPWs:
- Connect the USB cable of the VNA to your computer. Turn the VNA ON.
- Launch the S2VNA software.
- Connect the N to SMA cables to each one of the ports of the VNA.
- Make sure you have the stimulus settings ready i.e. set the start, stop frequencies and the number of points before you calibrate. (1MHz to 8GHz for CMT 804U).
- Now, go ahead and make a Full 2-Port calibration.
- Once you are done with the calibration, go ahead and connect the cable to be measured (DUT) to the VNA cables.
- Change the number of traces to 4. To do so, click on Display > Num of Traces and enter 4.
- Allocate the traces by following Display > Allocate Traces and click on the 8th option.
- Make sure that the parameters in the four traces are S11, S21, S12 and S22.
- Let the formats of the various S parameters be as follows: S11 and S21 (Log Magnitude), S12 Delay and S12 phase. Vary the various S parameter to measure also S12 (mag and phase) and S22. Estimate the return loss. (Note: The value of return loss can be read using a marker search and setting it to the maximum. Similarly, the value of insertion loss can be read using a marker search set to minimum).
- Now separate the two CPW from one another as is Figure 8.3. Each CPW is consisted has one SMA connector.
- Place the two CPW on top of each other (Figure 8.4). Input the signal from one SMA and
measure the transmission through the other. Assess the S-parameter, loss, phase change and
time behavior. Secure the two using a tape. Is alignment of the two important?
- Flip the CPW and position them as in Figure 8.5 The coupling would be stronger because the
separation is much smaller. Use, paper, plastic or any thin sheet and assess the difference in the
coupling strength as a function of frequency. Input the signal from one SMA and measure the
transmission through the other. Assess the S-parameter, loss, phase change and time behavior.
Secure the assembly using a tape.
Lab Report
- What is the value of the return loss (S11) you measured?
- What is the value of the insertion loss (S21) you measured?
- Include a screenshot of your measurements with all four S parameters in it.
- What was the value of the delay and impedance in your measurement?
- Compare your experimental data with simulations using HFSS, Comsol, MultiSim, or AWR in the frequency and time domains.
- How does the coupling depend on the interaction length? How does it depend on the separation between the CPWs?