Introduction: What is a filter?

Filters are two-port networks that are used to remove or propagate, certain frequency bands depending on the application. For example, in RF receiver applications, filters are frequently used to select an intermediate frequency and reject other signals before the filtered signal is processed by a demodulator.

Types of filters

There are four basic types of filters: low-pass, high-pass, bandpass and bandstop. A visual description of the filters can be shown below.

Types of filter design

Different filter designs have different response characteristics and are chosen to meet varied requirements. Listed below the different filter designs and their characteristics:

1. Butterworth Design:
   A ripple free pass band and a smooth stop band characterize this design. Increased attenuation is achieved as you move away higher in frequency. The downside for this design is that it uses more components than Chebyshev or Elliptical designs, which makes it less economical in applications that does not require a ripple free pass band. 


2. Chebyshev Design:
   A predetermined amount of pass band ripple is used to design filters that meet Chebyshev characteristics. The roll off and the stop band is smooth and approaches infinity as the frequency moves away from the band edges. It requires lesser number of elements to achieve similar shape factor as compared to a Butterworth design. Therefore, it is more economical and hence used more commonly used in filter designs. A good quality factor is required for such filters, typically a Q of 250 for inductors and 500 for capacitors. 


3. Elliptical Design:
   This also requires a predetermined amount of pass band ripple along with stop band ripple. Although these use the least number of elements required in achieving a desired shape factor compared to Chebyshev or Butterworth designs, the quality factor required for the elements are very high. As a result, the dynamic range of frequency elliptical filters can be used are limited by the elements’ Q. These filters are ideal for applications that require a very sharp roll off. Roll off ratio as lower than 1.01 at 40dB can be achieved using this. 


4. Bessel Design:
   Bessel filters are a kind of linear filters with maximally flat group delay and hence maximally linear phase response. For lowpass and narrow bandpass filter designs, the delay is flat throughout the pass band, but for wider band pass filters, special designs are used to achieve the group delay flatness. The downside of this is that the roll off is horrible with ratio of 2 at 13 dB and has a very poor VSWR. 


5. Gaussian Design:
   The step and impulse response of a Gaussian filter has ZERO overshoot while minimizing the rise and fall time. The delay response is almost similar to that of a Bessel filter, except that it has a bump at the center frequency. The cutoff frequency for Gaussian is usually specified as the 6 dB cutoff or 12 dB cutoff.

General Best Practices

1. It is always a good practice to warm up the VNA before using it to get accurate measurements. 
2. It is also important 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 -30 dB or -40dB). 
3. Always make sure to use a torque wrench to secure the connections made. 
4. Also make sure that the VNA is in an ESD (Electrostatic Discharge) safe environment and if possible, wear an ESD wrist wrap.

Calibration

A short summary for a Full 2-Port Calibration for CMT804U is given below (see also Lab 2 - calibration of VNAs).

1. Before you begin the actual calibration procedure, it is always a good practice to have the stimulus settings ready and then start the calibration.
2. To begin the stimulus settings, click on the stimulus option on the sidebar and set the start frequency to 1 MHz and stop frequency to 8 GHz.
3. Next, set the number of points to 401 or higher. Leave the IF bandwidth unchanged (i.e. 10 KHz). Play with the intermediate frequency setting and check the effect on your measurements. 
4. The calibration kit definition is where the instrument is told the actual, known characteristics of the calibration standards. Each calibration kit has its own known characteristics. The Kit number is indicated on the N-Type cross kit (N911/912). Choose that number from the drop down window. 
5. For a full two port calibration, follow the steps below:
• On the main menu in the sidebar go to Calibration -> Calibrate -> Full 2-port Cal
• To perform the calibration, connect the “Open” standard to the end of the cable on Port 1.
• Click the “Open” button on the screen. It should say “calibration in progress…” followed shortly by a checkmark on the left part of the button.
• Repeat (a) and (b) with the Short and Load standards with the cable attached to Port 1.
• Similarly, repeat (a), (b) and (c) for Port 2.
• Now connect the “Thru” standard between the two ports through the cable. When it’s attached, click the “Port1-2 Thru” button and then click on the Subclass 2 UnThru option.
• When there is a check mark next to each of the seven standard names click “Apply.”The program will process the measurements, computing differences between the measured characteristics and the known correct characteristics provided in the calibration kit definition earlier. These differences are due to non-idealities of the VNA itself and losses in the cables and adaptors used. The error correction will automatically be enabled.


6. Correction option under calibration should now be ON. If it says OFF, click once and it should now be activated. This will apply the calibration settings to the measurements being made.

Note: The Kit number is indicated on the N-Type cross kit (N911/912)

Pre-Labs

1. What is quality factor?
2. List the applications of a bandpass filter.
3. What is cut-off frequency of a filter? Explain.
4. In your own words, explain what filter gain is.

Objectives

1. To understand the characteristics of bandpass filter and how to measure the characteristics using a VNA. 
2. To understand the importance of using a VNA for high-frequency measurements. 
3. Understand the importance of simulations

Lab Procedure for Filter Characterization

(Filter characterization video link, https://coppermountaintech.com/video-measuring-a-filter-with-the-university-kit/)

1. Turn the VNA on and open the S2VNA software. Now connect the cables to both the ports of the VNA. 
2. Make a Full 2-port calibration by using the steps given above in this document. Do not rely on past calibrations due to change of connectors and VNA model - always start a new experiment with new calibration. 
3. Once your device is calibrated, connect the band pass filter between the two ports of the VNA. 
4. To see all the S parameters (S11, S12, S21 and S22), simply click on the Display option on the sidebar menu and change the Num of Traces to 4. 
5. Click on Allocate Traces and choose the cross plate (4 traces). 
6. You will now see four traces on your screen. Make sure that the traces are S11, S12, S21 and S22. The formats for various S parameters are: S11 and S21 is Log Mag, S12 is Phase and S22 is Smith Chart. 
7. To enable the marker readings for S21, simply click on the S21 marker first and then click Markers, > Marker Math > Bandwidth search ON. Once you enable this, you will see the various bandwidth readings as shown in Figure 2 below. Remember that a bandwidth is measured at 3-dB from the curve's plateau.







8. The graphs of various S parameters measured should be shown. 
9. Measure the characteristics of at least two filters (LP, BP or HP provided).

Lab Report

1. Attach a screenshot of your S parameter measurements of your filter.
2. At the center frequency of your bandpass filter, what was the value of your S11 and S21. What does this mean?
3. Discuss how the values would have differed if calibration was not performed.
4. Include a copy of ideal response of a bandpass filter and compare it with your measured response.
5. How is return loss of a filter related to its insertion loss? Hint: Explain using the law of conservation of energy. Comment on the difference between voltage loss and power loss.
6. Use HFSS, Comsol or AWR to simulate a generic filters of the kind you have measured. What are the key parameters to observe? (Many of these simulations tools have tutorials or demo applications)
7. Experimentally obtain and simulate the filter in the time domain and compare between experiments and simulations.