# The Q factor calculation for the two-port SAW resonator

1. Oct 13, 2011

### feiyuzhen

In some papers, I found that the Q of resonator, i.e. one-port SAW resonator, can be calculated with the formula 1/f0*(diff(phi(f),f)@f=f0),phi(f) is the phase of impedance,
I have tested one one-port saw resonator with the network analyzer agilent4395A under the impedance mode, then process the phase-frequency data and the modulus of impedance with the relation of frequency, the Q value calculated from the formula above is similar with the ratio between working frequency and 3dB band.
Then for the two-port SAW resonator, usually can be tested under the network mode, and so I would got two data groups, one is insertion loss data in a frequency band, other one is the phase data in a frequency band, can the Q factor be calculated with the formula that for the one-port resonator?
I have calculated the Q value from the two data groups,one is using formula f0/Δf(3dB band),other one is using the formula above,
The results does different,but the difference is small.
I want an explanation whether it is correct for the phase-frequency formula used for the Q factor calculation for the two-port SAW resonator.
help,thank you in advance.

2. Oct 13, 2011

### f95toli

*How is the resonator connected? Do you get a notch or a peak response?
*Are you looking for the loaded or unloaded Q?
*The best way to calculate Q is usually to plot the data in the I-Q plane and then fit a circle to it using a least-square fit. The fitting parameters for the circle can then be used to calculate the Q using whatever formula is relevant for your situation (1-port, 2-port, parallel or series connection etc).

*If you are only interested in the loaded Q (and don't need to worry about the coupling) one can usually get away fit just fitting to a standard Lorentzian.

If you want the full details you should try to find a copy of the book "Q Factor" by Kayfez

Also, J don't think there is any reason for why you would need to look specifically at paper for SAW resonators, Q is Q regardless of what type of resonator you are measuring.

3. Oct 14, 2011

### feiyuzhen

Thank you for your post.
1.A power splitter connected to the Agilent4395A, then one port of it is connected directly to the network analyzer, that's the reference channel.The other port is connected to the input of the two-port SAW resonator, and the ouput of the resonator is connected to the network analyzer, that's the test channel.Of course, all the wire are coaxial line. Then with the ratio of the power from the two channels, we can get the insertion loss and the phase-frequency figure. For the two-port SAW resonator, I got a peak response.

2. There are three ports used on the 4395A. 1st one is connected to the power splitter,2nd one is connected to splitter too and 3rd one is connected to the SAW resonator. The port connected to the splitter is like a power supply and the internal impedance is 50ohm, the other two ports are like two resistor and their impedance are also 50ohm. I think I'm looking for the loaded Q.

3."The best way to calculate Q is usually to plot the data..." what data? "...in the I-Q plane..." current-Qvalue plane? and then, how to calculate?

4.you're right, the IL(insertion loss)-freq figure can be fitted to a standard Lorentzian, but
I want calculated the Q value from phase-freq figure. The reason is below. I can tuned the scan frequency band on the 4395A, if I set the band equal to 0, then the network analyzer works like a single frequency source, and then I enlarger the IL, I can see the noise at that frequency point,
but, for the IL-freq figure I can't understand the meaning of it, the noise of IL at that point?
I don't know, but for the phase-freq figure, the meaning of it is the noise of the phase at that point.Then the calculated slope of the phase-freq figure near that frequency point can be used for calculated the equivalent frequency. For example, the slope is 1 degree/Hz,the noise band is 0.1 degree,then the equivalent frequency is 0.1Hz. That's why I want to know whether the formula for the one-port SAW resonator can be used for the two-port SAW resonator.

Finally, I can't find the copy of the book "Q Factor" by Kayfez, can you help me, I'm very appreciate for that.

4. Oct 14, 2011

### biff44

Q for a 1 port resonator is as defined in your original post. But "Q" for a 2 port is a somewhat undefined concept.

If you want to treat the 2 port saw bandpass response as the resonator in a transmission type oscillator, then yes, measuring the 3 dB down points will relate to a "Q" that has some meaning. For example, you could use that "Q" in Leesons equation for a phase noise estimate.

Note: when you measure ANY narrowband resonator with a network analyzer, you need to do so carefully. You want to reduce the IF bandwidth, and slow down the sweep time, or you may get very erroneous results.