Re : modeling 4461 card

[MisterDAQ]

Hi EBL,

I began to study your doc one week ago. It's quite interesting, but quite new for me.
I'm ok with the one-port calibration. I try to do the same thing as in your work. But, I try to use
the usual model u=zi instead of reflection/refraction theory. They say that it is quite the
same thing except that the refraction model is only based on voltage, wich is quite interesting
for us, because we can only measure voltage.

I do not know If you are familiar with such calculations.

My first problem is the following: if I want to consider my R,L,C before the dut, I can use Thevenin's
theorem and assume that my circuit is equivalent to one generator with a complex impedance. In this
case, one measure using a "Load" is sufficient to find the equivalent impedance. So why 3 measures ?
Or an equivalent question : why must we choose to model the fixture using a two port device ?

I do not really succeed in modeling the fixture with a two port or a one port device...  Maybe the
full differential DAC/ADC force you to select a two port model ?

thx for the help 🙂



Message Edité par MisterDAQ le 01-28-2008 08:59 PM

[EBL]

Hi, MisterDAQ.

The article I pointed you to was the most applicable I could find at the time. Don't be confused by the fact that it describes the two port system - be assured that we need only one port in order to do impedance measurements.

The reason to prefer s-parameter treatment of this measurement problem is that the impairment caused by the fixture (wire length, inductance, capacitance, everything) is most easily modeled with flow-graph theory. That's not to say other methods won't work, but I find that it keeps the mathematics fairly simple. For instance, s-parameters happen to handle both 0 impedance and infinite impedance at the same time somewhat gracefully; the same cannot be said about most other methods.

Regardless of what method you use, there are fundamentally three degrees of freedom in the characterization of the fixture parasitics. That's why three measurements are needed in order to fully calibrate the system. For instance, the three variables might be chosen as series fixture impedance, parallel fixture impedance, and absolute impedance. We can actually choose any three independent variables, but the beauty of the method is that you don't have to decide explicitly at any time what those three impairments are, as long as you calibrate at three distinct points. The mathematics takes care of the rest.

You don't even have to calibrate at short, open, and known load impedance. You could choose any three (known) points and still get workable results, but these three happen to be the most convenient, and they give the most mathematical leverage, being as far apart in impedance space as possible.

Cheers,
Ed

[MisterDAQ]

At the beginning... I turn to be a mathematician, so I clearly understand your mathematical argument.

But, when I turn to electronics, it's more difficult. For instance, what do you mean by :

  * series fixture impedance, parallel fixture impedance, and absolute impedance

[MisterDAQ]

Another question that bothers me : in the fixture, you make two voltage measurements using two inputs. I do not see if that corresponds to the model described in the doc of HP. In the example they present, they just measure the voltage at the DUT, if I understand well. Why do you use two voltages ? Do you use the formulae given in this document "as is", or have you completly rewritten a new system of equations for your fixture ?

Sorry, I'm very curious

thx for you help

Message Edité par MisterDAQ le 01-29-2008 06:42 PM

[EBL]

>>But, when I turn to electronics, it's more difficult. For instance, what do you mean by :

  * series fixture impedance, parallel fixture impedance, and absolute impedance<<

Well, these are just examples. But suppose the imperfections in your measuring fixture were that it had some resistance that always appeared in series with the DUT (for example, that limited you to 0.5 ohms), some resistance that always appeared in parallel with your DUT (for example, that limited you to 1 Mohm), and an absolute calibration error (for example, such that impedance always read high by a factor of 1.2). Those would be three independent impairments. It's never going to be that simple in reality, but you get the idea.

>>Another question that bothers me : in the fixture, you make two voltage measurements using two inputs. I do not see if that corresponds to the model described in the doc of HP. In the example they present, they just measure the voltage at the DUT, if I understand well. Why do you use two voltages ? Do you use the formulae given in this document "as is", or have you completly rewritten a new system of equations for your fixture ?<<

Technically s-parameters deal with a "wave," which consists of a voltage component and a current component. These two components are related by the reference impedance of the system. In the case of most RF systems, the reference impedance is 50 ohms. In our case, we've chosen 1 kohm as our reference impedance.

We need to measure the forward wave and the reflected wave, compute the ratio of the two, correct the result, and transform the result into impedance. Since the voltage on channel 0 is measured on the generator side of the 1 k test resistor, it will be the same almost independent of whatever the DUT impedance is. So that's essentially measuring the forward wave, or at least a signal that's proportional to it. The extent to which it's not doing that job perfectly will be corrected in the calibration.

The reflected wave is determined by measuring the difference between the voltage on the DUT side of the test resistor and 1/2 the voltage on the generator side of the resistor. That forms an impedance bridge which measures how far off the DUT is from 1 kohm, which happens to be proportional to the reflected wave. Again, the extent to which it doesn't do that job perfectly is corrected later in the calibration arithmetic.

All of the arithmetic is contained in these two subVIs:

DSA4461 Refl Acq Multi-Tone.vi
DS11CorrCalc.vi

The s11 data that comes out of those is transformed into impedance.

Cheers,
Ed L.

[MisterDAQ]

Dear EBL,

I read a lot of pages speaking about HF. I'm now a bit familiar with these notions.
But, some points in your explanations remain difficult for me...


In the case of most RF systems, the reference impedance is 50 ohms. In our case, we've chosen 1 kohm as our reference impedance.

The 50ohms impedance in RF corresponds to the ration between the amplitudes of the E and the H fields.
That does not correspond to the resistance of the BNC cable. In your fixture, you use a 1k resistor in order to
simulate an RF impedance of 1k... I'm desperately overtaken by this assumption 😞


Since the voltage on channel 0 is measured on the generator side of the 1 k test resistor, it will be the same almost independent of whatever the DUT impedance is. So that's essentially measuring the forward wave, or at least a signal that's proportional to it. The extent to which it's not doing that job perfectly will be corrected in the calibration.

that's ok



The reflected wave is determined by measuring the difference between the voltage on the DUT side of the test resistor and 1/2 the voltage on the generator side of the resistor. That forms an impedance bridge which measures how far off the DUT is from 1 kohm, which happens to be proportional to the reflected wave.

I do not see where the value 1/2 comes from. You quickly explain this phenomenom by analogy. Is it really so simple ? You seem to migrate from the HF to the Low Freq without difficulty. Is there any trick ? Or Is it an experience of several years spent in measurements ?

thx again for you precious help

Message Edité par MisterDAQ le 02-06-2008 10:00 PM

Message Edité par MisterDAQ le 02-06-2008 10:00 PM

[EBL]

Hi, MisterDAQ.

If I seem to migrate freely between RF and low frequencies, it's because as a mathematician I see no difference between the two. The signal processing is the same in both cases; it takes no interest in the particular frequencies used. And in fact, RF actually extends down into the measurement range of the 4461; take for example the 60 kHz time signals that are broadcast in various parts of the world. Those could be handled easily by the 4461.

As for 1 kohm versus 50 ohms: there is nothing magic about either impedance. 1 kohm happens to be about in the center of the range of impedances I tend to be interested in (say, 0.1 ohm to 10 Mohm), so it makes a good choice for a reference impedance. In RF, 50 ohms is commonly chosen as a reference impedance and so most coaxial cables, circuit board traces, and impedance bridges are made at that impedance. But in either case the reference impedance could be changed and the math would take care of everything.

The factor of 1/2 comes from the fact that a resistive-divider bridge is formed out of the fixture impedance and the DUT. If the DUT is the same as the fixture impedance, then the voltage is divided exactly by 2. Hence when Ch1 sees 1/2 the voltage of Ch0, the "reflection" with respect to 1 kohm is zero. Any difference from 1/2 measured at Ch1 indicates a "reflection," that is, some impedance other than 1 kohm. The actual impedance is calculated from that difference (after calibration correction, of course). Take a look at the code to see for yourself - I promise it's not too complicated.

Cheers,
Ed

[MisterDAQ]

Hi EBL

I'm always digging the secrets of HF. You completely mix the 50 impedance in HF and you 1k impendance in BF. They are physically completely different and that bothers me. But, you seem to consider that they are mathematically equivalent ?

I must consult your vi but at the moment the computer migrates to winxp and Im unable to connect to it. In a few days this will be done. Meanwhile, I continue to read some information on s parameters.

Today, I find a document that speaks about the three errors to measure when testing a one port device. Apparently, only the s11 parameter is estimated for this operation. Errors are modeled relative to this coefficient. So, they obtained :
s11m = Ed+Er*s11/(1-E*s11)  EQ1

where E denotes the amplitude of the sine, s11m the measured s11, and where Ed Er s11 are the three unknowns. The three measures (open,short,loaded) allow to determine the three coefficients. I do not know their name in english (the doc is in french), maybe : directivity error.., transmission error...

I suppose, but I'm not sure, that EQ1 is the model you use in your calculations ? That's the question for today 🙂

thx again


Message Edité par MisterDAQ le 02-12-2008 07:19 AM

Message Edité par MisterDAQ le 02-12-2008 07:20 AM

[MisterDAQ]

Hi again,

I just understand one thing. You absolutely do not consider any capacitance or resistor coming from the NI card. In you circuit, you operate as if you only have one 1k resistor. Parasite capacitances and resistors from the DAC and the two ADCs are modeled in the three errors of the s-parameters : directivity, source match, reflection tracking. Am I right ?

At the beginning, I considered that you model the inner components of the DAC and ADC using one s matrix for each of them. So, you have to use 3 S-matrices for the all fixture. At the end, your circuit is only a 1k resistor ?

Message Edité par MisterDAQ le 02-12-2008 08:34 AM

[EBL]

Bonjour MonsieurDAQ,

>>I'm always digging the secrets of HF. You completely mix the 50 impedance in HF and you 1k impendance in BF. They are physically completely different and that bothers me. But, you seem to consider that they are mathematically equivalent ?<<

They are, indeed. RF uses 50 ohms as the reference impedance, and in this case we use 1 k as the reference impedance (though it is not some generally accepted standard like 50 ohms is).

>>So, they obtained : s11m = Ed+Er*s11/(1-E*s11)  EQ1<<

>>I suppose, but I'm not sure, that EQ1 is the model you use in your calculations ? That's the question for today<<

That's in essence, though not exactly, what's being done in DS11CorrCalc.vi.

>>I just understand one thing. You absolutely do not consider any capacitance or resistor coming from the NI card. In you circuit, you operate as if you only have one 1k resistor. Parasite capacitances and resistors from the DAC and the two ADCs are modeled in the three errors of the s-parameters : directivity, source match, reflection tracking. Am I right ?<<

That's correct. I would add only that I think the three independent errors I'm using are not exactly those, but equivalent by mathematical transformation.
 
>>At the beginning, I considered that you model the inner components of the DAC and ADC using one s matrix for each of them. So, you have to use 3 S-matrices for the all fixture. At the end, your circuit is only a 1k resistor ?<<

In essence, the model of the fixture impairment (including the DACs, ADCs, cables, capacitors, wires, fingers, noses, and all) is one s-parameter matrix. Note that an s-parameter matrix contains four elements, while we only have three variables. The fourth (forward coupling, s21) is normally arbitrarily chosen to be 1, without loss of generality. Sometimes the error is distributed between the s21 and s12 elements of the impairment network model.

Cheers,
Ed