I was referring to the link https://www.analog.com/media/en/technical-documentation/application-notes/75731446AN264.pdf and https://www.analog.com/media/en/technical-documentation/data-sheets/AD2S1200.pdf  to understand and interpret dynamic characteristics of RDC.  My questions are

1. Can we simulate the transfer function specified in AD2S1200 datasheet and infer characteristics such as tracking rate, BW, Ka?

2. How is tracking rate related to bandwidth? Can we have higher tracking rate for lower bandwidth?

3. If input shaft is rotating at constant velocity of 500 rps, should we have bandwidth of 500 Hz? I have confusion? are there any analytical methods to arrive at proper figures

4. Suppose 10kHz ref frequency is chosen, will tracking rate change?

5. Although Type 2 will have zero velocity lag, it will experience lag for certain period before catching up. How to estimate this period. Is it same as settling time?

[edited by: @skowalik at 1:54 PM (GMT 0) on 5 Feb 2020]
Parents
• Ram,

Apologies for the late reply on this post.   See my responses below.

1. Can we simulate the transfer function specified in AD2S1200 datasheet and infer characteristics such as tracking rate, BW, Ka?

The quick answer is that you can implement the AD2S1200 transfer function in Simulink or equivalent modelling environment for your purposes as this will provide the most dynamic environment for you purposes.   I

2. How is tracking rate related to bandwidth? Can we have higher tracking rate for lower bandwidth?

Loop bandwidth will determine the ability of the control loop to track the input and respond quickly to changes in position, recall that the objective of the R2D loop is to drive the angular error to 0 for a constant velocity.   To ensure the measurement system can respond quickly to changes in the position we must have sufficient bandwidth to avoid excessive latency in reporting the new position.  If the loop is too slow (insufficient BW) then there will always be an error in the reported position.

3. If input shaft is rotating at constant velocity of 500 rps, should we have bandwidth of 500 Hz?

As described in question 2 we should always have more bandwidth than the maximum tracking rate requires to avoid lag in the response of the loop to the input.

I have confusion? are there any analytical methods to arrive at proper figures

4. Suppose 10kHz ref frequency is chosen, will tracking rate change?

The tracking loop uses the demodulated quadrature signal to estimate the angular position and thus is immune to carrier selection.

5. Although Type 2 will have zero velocity lag, it will experience lag for certain period before catching up. How to estimate this period. Is it same as settling time?

That is correct.

• Ram,

Apologies for the late reply on this post.   See my responses below.

1. Can we simulate the transfer function specified in AD2S1200 datasheet and infer characteristics such as tracking rate, BW, Ka?

The quick answer is that you can implement the AD2S1200 transfer function in Simulink or equivalent modelling environment for your purposes as this will provide the most dynamic environment for you purposes.   I

2. How is tracking rate related to bandwidth? Can we have higher tracking rate for lower bandwidth?

Loop bandwidth will determine the ability of the control loop to track the input and respond quickly to changes in position, recall that the objective of the R2D loop is to drive the angular error to 0 for a constant velocity.   To ensure the measurement system can respond quickly to changes in the position we must have sufficient bandwidth to avoid excessive latency in reporting the new position.  If the loop is too slow (insufficient BW) then there will always be an error in the reported position.

3. If input shaft is rotating at constant velocity of 500 rps, should we have bandwidth of 500 Hz?

As described in question 2 we should always have more bandwidth than the maximum tracking rate requires to avoid lag in the response of the loop to the input.

I have confusion? are there any analytical methods to arrive at proper figures

4. Suppose 10kHz ref frequency is chosen, will tracking rate change?

The tracking loop uses the demodulated quadrature signal to estimate the angular position and thus is immune to carrier selection.

5. Although Type 2 will have zero velocity lag, it will experience lag for certain period before catching up. How to estimate this period. Is it same as settling time?

That is correct.

Children
• Hi

Thank you for those answers. But not very clear between relation of BW to tracking rate. How much should be the bandwidth to meet the tracking rate. I think resolution, BW and tracking rate are related to each other. I wanted to know the basis of their relation. For example, AD2S44 has 14 bit resolution, BW: 100Hz and Tracking rate of 20 RPS for 400Hz reference frequency. In addition, it has accuracy of 4 arc min. I see a proportion here. How to predict tracking rate from transfer function. Also please define accuracy in this context

• Ram,

The BW is set by the dynamics of the R2D loop and thus is fixed based on the selected resolution and the master clock frequency.   Thus for the settling time(s) quoted in the datasheet you can expect the angular velocity and angular position (when fully settled) to match the specified accuracies.   If you need a higher tracking rate for a given resolution you can increase the master clock but you will also increase the bandwidth of the loop filter.

I hope that clears up any confusion and I apologize for not clearly stating the relationship is fixed by the dynamics of the tracking loop in my previous response.

Sean

• Hi

1. In article specified in my first post, I see an example that 1MHz master clock if used can give 1MHz/4096 rev/s for 12 bit R2D. Now it appears that tracking entirely related to clock rather than bandwidth. I wanted to know if there are empirical method to arrive at the desired tracking rate or is it purely experimental in nature. For example, the parameter Ka, BW can easily be inferred from the TF and bode plot. But I do not see the same relation applicable for tracking rate. I find a lot of disparity in this parameter when comparing with multiple datasheets of R2D even from your competitors. There is no clear definition.  I would highly appreciate answer with data. For example, if BW is set to say 20Hz, how could we arrive at max tracking rate of the converter (without using software calculator)?

2. How do we check BW specifications at the output of R2D. The article says 5 degree amplitude ( that's fine). Should this signal be superposed with original quadrature signal?

3.  My inputs would not exceed100 rps, what should be Ka to tolerate say 1 degree of error for 10ms? How to calculate this factor and how to select R2D for this specification?