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Modeling a Terminating Impedance

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deef

Fri Feb 25 2011, 07:30PM

Registered Member #207 Joined: Sat Feb 18 2006, 05:14PM
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Posts: 45

Hey everyone,

Who's ready for "Dumb Question of the Day"? I can't remember the correct method of modeling a device with an equivalent Terminating Impedance in a signal path. And, now that i'm thinking about it, my mind is playing games with me.

Refer to the image for further details, but basically:

Z1 = Represents the impedance of a signal source and bunch of passive filter elements, etc.
Z2 = Represents the impedance of some kind of ac-coupled gain stage.

The resistor and capacitor, in parallel, in between Z1 and Z2 represents a crystal SAW filter that is specified to have a "Terminating Impedance = 1.5kOhm//-1.2pF". I'm looking to model the filter in SPICE to determine whether or not the impedance matching portions of Z1 and Z2 are coupling to the SAW filter properly. However, I can't figure out how the 1.5kOhm//-1.2pF impedance of the filter should be represented.

Is Option A, or Option B correct?

1298662122 207 FT0 Terminating Impedance

Mattski

Sat Feb 26 2011, 12:00AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

I don't think either is correct, but B is closer. "Terminating impedance" means impedance to ground, i.e. Zin or Zout. And input impedance is defined with a specific impedance for Z2, and output impedance depends on Z1. The terminating impedance is typically specified in a 50ohm environment, so if Z1 and Z2 are both close to 50 ohms then you're probably okay.

So the actual network will be something like Z1--shuntRCnetwork--saw filter network--shuntRCnetwork--Z2. If at the resonant frequency the SAW filter were to drop out (no loss, no delay) then you would end up with picture B but with half the resistance and twice the capacitance. There's a good chance this will be a reasonably accurate assumption if you're at a low frequency.

Does the manufacturer provide s-parameters of the filter or an equivalent resonant network circuit?

deef

Sat Feb 26 2011, 12:39AM

Registered Member #207 Joined: Sat Feb 18 2006, 05:14PM
Location:
Posts: 45

Thanks for the reply, Mattski. Clearly, i'm a little lost.

Alright, first off, I need to correct a mistake I made in my first post. It's not a "crystal saw" filter. That was a typo. I'm, in fact, working with a monolithic crystal filter. Also, for reference, my working frequency is 110MHz.

Unfortunately, the manufacturer doesn't supply s-parameters. However, I was able to dig up the following image from an application note. (See Below). I have a couple questions about your explaination.

1) ["Terminating impedance" means impedance to ground, i.e. Zin or Zout.]... What do you mean Zin *or* Zout? It's one or the other, but not necessarily both? :)

2) [So the actual network will be something like Z1--shuntRCnetwork--saw filter network--shuntRCnetwork--Z2]... What shuntRCnetwork are you referring to? Is this network added for impedance matching? Or is that what they're specifying in the datasheet as "1.5kOhm//-1.2pF"?

Finally, now that i'm looking at the image in their application note (attached below), what are resistive and capacitive elements that share a node with "Zt" on either side of the MCF? Are these the elements represented as "Terminating Impedance = 1.5kOhm//-1.2pF"?

Again, thanks a bunch for your help.

Mattski

Sat Feb 26 2011, 03:47AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

deef wrote ...

1) ["Terminating impedance" means impedance to ground, i.e. Zin or Zout.]... What do you mean Zin *or* Zout? It's one or the other, but not necessarily both? :)

It's both Zin and Zout. The filter is almost certainly symmetric, so S11=S22=(Zin-Zo)/(Zin+Zo)=(Zout-Zo)/(Zout+Zo).

wrote ...
2) [So the actual network will be something like Z1--shuntRCnetwork--saw filter network--shuntRCnetwork--Z2]... What shuntRCnetwork are you referring to? Is this network added for impedance matching? Or is that what they're specifying in the datasheet as "1.5kOhm//-1.2pF"?

The shunt RC network I refer to is the 1.5k//-1.2pF network, which should be Zin and Zout of the filter.

wrote ...
Finally, now that i'm looking at the imagine provided from their application note (attached below), what are resistive and capacitive elements that share a node with "Zt" on either side of the MCF? Are these the elements represented as "Terminating Impedance = 1.5kOhm//-1.2pF"?

The R after the signal generator and the R on the far right are the signal generator source resistance and load resistance respectively. The two capacitors in the schematic are probably added for impedance matching, since they will cancel out the negative effective capacitance on the input of the filter. If the two R's are made 1.5kOhm and the C's are +1.2pF then the source and load will be matched to the filter. I'm not sure what the LM means. I'm also assuming the input impedance has a negative capacitance, seems reasonable since it's just a circuit model of a physical resonating element, I know there can be negative effective capacitances in some waveguide situations.

wrote ...
Again, thanks a bunch for your help.

No problem :)

deef

Sat Feb 26 2011, 08:33AM

Registered Member #207 Joined: Sat Feb 18 2006, 05:14PM
Location:
Posts: 45

Great! I think I'm starting to understand now.

Just to confirm my understanding, here's a scenario. Referring to the graphic in my original post, if the crystal filter were sandwiched between Z1 and Z2, for a situation of matched impedance, the following must be true:

- The output impedance of Z1 should be 1.5kOhm//-1.2pF
- The input impedance of Z2 should be 1.5kOhm//-1.2pF

With this established, you'd be able to couple the most power into, and out of, the crystal filter. Am I on the right track?

Mattski

Sat Feb 26 2011, 03:16PM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

deef wrote ...

- The output impedance of Z1 should be 1.5kOhm//-1.2pF
- The input impedance of Z2 should be 1.5kOhm//-1.2pF

Just about right, the resistance is correct but the capacitance of Z1 and Z2 would need to be 1.2pF because when you have reactive as well as resistive components the condition for max power transfer is a conjugate match where the resistance match but the reactances have equal magnitude and opposite sign.

deef

Sat Feb 26 2011, 08:59PM

Registered Member #207 Joined: Sat Feb 18 2006, 05:14PM
Location:
Posts: 45

Oh, right. Of course -- yeah. That was a silly mistake on my part.

Thanks for your help! Problem solved.

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