# Clarification Regarding Operating Principle of AD7745 IC - Single Ended Floating Sensor

#### KlausST

##### Super Moderator
Staff member
Hi,

A rather short and vague question....you did not put much effort in it.

You don't tell what you already did understand and what details you are interested in, so we don't know on what we should focus on.

We usually have the knowledge from the datasheet and other informations the manufacturer provides on the internet. Did you read them, too?
You surely don't want us to read this all this informations and write them down here.
So, please tell us more exactly what you want to know.

Klaus

The device is a capacitance sensor, a capacitance meter.

#### _pA89

##### Junior Member level 1
Hi KlaussST,

The Information I Need is Simple:

To Complete/Correct and Map the given Equation to Figure 2 CDC Architecture. (Just the Operating Principle - Can you point to right Information in Internet?)

otherwise we cant understand :
1. How (much) Scaling Factor F reduces Accuracy of Measurement. (does it?), Can Scaling Factor be made arbitrarily high?
2. Will Value of Excitation Voltage(Can I see Ringing, reduced Voltages @EXCA pin) affect the Measurement Results
3. Scaling 9pF capacitor into 4pF range producing negative capacitance Results (CAPDAC=0) (does it?)
4. Why Scaling cant be done by External Excitation Signal as pointed out in this Post.

and so on...

P.S:
1. The IC is used for Measurement of Capacitance of a sensor.
2. Yes I did read Information Provided by Manufacturer. -{1. Datasheet-AD7745, 2. AN-1055, 3. AN-1585, 4. AN-1301} (Anywhere to put more effort?)

#### KlausST

##### Super Moderator
Staff member
Hi,

This is no equation.
It just says that the measured C_Sensor value depends on the given paramaters
But there is no mathematical formula "how" the value depends on the parameters.

I come back later..

Klaus

#### stenzer

Hi,

1. How (much) Scaling Factor F reduces Accuracy of Measurement. (does it?), Can Scaling Factor be made arbitrarily high?
I created once a range extension circuitry for the AD7143 (eight channels, single excitation signal) based on the considerations in [1]. The "bulk" capacitance was ~100 pF, which was compensated by the internal OFFSET register (-> set to a zero reading), as I was only interested in a capacitance increase. The range extension was designed to be operated up to several hundrets of pF, but in the end it has only shown a linear relation in the lower range (+ ~200 pF).

3. Scaling 9pF capacitor into 4pF range producing negative capacitance Results (CAPDAC=0) (does it?)
No, therefore you are calculating your scaling factor which leads to a reduction of your excitation signal amplitude. As you reduce the excitation amplitude, you can increase the capacitance as $Q = C \cdot V$. This is the basic idea behind the method described in [1], and is mentioned in section "Circuit Discription" in the beginning of page 3.

4. Why Scaling cant be done by External Excitation Signal as pointed out in this
This is quite tricky due to the realization of the CDC. As the excitation signal frequency has to be consistent with the internal switching which is performed due to the
$\sum \Delta$ topology. One might try to use the excitation signal itself to trigger an external circuitry, to maintain the required frequency and to allow an adjustable excitation voltage. In [2] measurement results of different AD7745 excitaion frequencies (different ICs) are listed, and the individual frequencies between the ICs differ. In [2] they also tried to use one external excitation source for multiple AD7745. So it seems an external synchronisation circuitry seems to be a minimal criterion to use an external excitation signal source in combination with a SINGLE CDC.

[1] https://www.analog.com/media/en/technical-documentation/application-notes/AN-1585.pdf
[2] https://ieeexplore.ieee.org/document/7969853

BR

#### _pA89

##### Junior Member level 1
Hi stenzer, thanks for quick response...
No, therefore you are calculating your scaling factor which leads to a reduction of your excitation signal amplitude.
-> The Results gets negative when you just interchange R1, R2 Resistors ? (I understood Q=CV, is the Device Ratio metric [1] or is it sensitive to Excitation voltage Level?)

+ ECX-Excitation Frequency(Signal Frequency) = 32KHz, Update Rate = [10,90] Hz (Nyquist Criterion)?

[1] Transducer/Sensor Excitation and Measurement Techniques - Analog Devices

#### FvM

##### Super Moderator
Staff member

Interchanging R1 and R2 is equivalent to inverting effective Excitation voltage. Due to phase sensitive processing of capacitor current this is equivalent to measuring a negative capacitance.

#### _pA89

##### Junior Member level 1
Hi FvM,
Interchanging R1 and R2 is equivalent to inverting effective Excitation voltage.
True, You are effectively inverting effective Excitation Voltage.
Due to phase sensitive processing of capacitor current ...
+ Need to understand operating Principle -any mathematical model ("processing" - is what needs to be understood) of AD7745 - CDC Operation (e.g. Ratio Metric method is used for Unknown Resistor Measurement Operation).

#### stenzer

-> The Results gets negative when you just interchange R1, R2 Resistors ?
Yes, but that wasn't your initial question. When sacling 9 pF into 4 pF, following the description in AN-1585, the result should be positive.

#### stenzer

Hi,

+ Need to understand operating Principle -any mathematical model ("processing" - is what needs to be understood) of AD7745 - CDC Operation (e.g. Ratio Metric method is used for Unknown Resistor Measurement Operation).

+ ECX-Excitation Frequency(Signal Frequency) = 32KHz, Update Rate = [10,90] Hz (Nyquist Criterion)?
As the CDC employs a $\sum\Delta$ topology it performs an oversampling respectively a decimation. The sample frequency is 32 kHz, so at each 32.25 µs a sample is taken. Due to the operation principle, a decimation is performed which is an averaging process. This reduces the final output/update data rate. Have a look on page 14 in [4], where this is mentioned for the AD7143.

[3] https://ieeexplore.ieee.org/document/6312573

#### _pA89

##### Junior Member level 1

1. [3] doesn't mention any Excitation Source (Square Wave)- EXCA?

2. Consider PCM1802 - Audio ∑Δ - ADC
* f_sampling=44 KHz (max=96KHz) = Output Data Rate------------------f_sampling_AD7745=? f_output_data_rate = [10,90] Hz
* f_oversampling = 64*f_sampling || 128*f_sampling (Page-11)-------------f_oversampling_AD7745 =?

• Susceptible to EM interference because there is no input filtering.
• It's not ratiometric. It relies on a 1.17V internal voltage reference.

#### stenzer

Hi,

1. [3] doesn't mention any Excitation Source (Square Wave)- EXCA?
It's a square wave, as this signal is used to charge your capacitor of interest.

2. Consider PCM1802 - Audio ∑Δ - ADC
A $\sum \Delta$ ADC samples/compares the signal at a high frequency (called sample frequency fs), which is a multiple of the output-data frequency fd times the decimation rate DR (or oversampling rate OSR). Have a look at [5]. The $\sum \Delta$ modulator provides a high bit stream with a (sample) frequency fs = fd • DR. This bit stream is then filtered/decimated and results in the output-data rate fd = fs/DR.

* f_oversampling = 64*f_sampling || 128*f_sampling (Page-11)-------------f_oversampling_AD7745 =?
The DR/OSR for the AD7745 is not stated. But according to [4] page 14, for the AD7143 the sample frequency should be 250 kHz (as the excitation frequency) to hold the stated equation (3 • 256 • 1/(250000) = 3.072 ms). Thus, the sample frequency for the AD7745 should be 32 kHz. Note, the unknown capacitor (sensor) is charged/discharged at this rate.

• Susceptible to EM interference because there is no input filtering.
• It's not ratiometric. It relies on a 1.17V internal voltage reference.
The AD7745 is a CDC and not a classical ADC, so the implementation of a filter structure is affecting your sensor/capacitve reading. Have a look on other CDCs from ADI as e.g. the AD7143 provides a shielding option, which might help to minimice EMC issues.

Ratiometric solutions would be a differential capacitive voltage divider approach [6] or an ASIC like the MAS6510 [7]. Multiple MAS6510 can also be used with a common external excitation source [3].

The voltage reference has a maximum deviation of $\pm$0.085 % at 25 °C, and a temperature dependent drift of 5 ppm/°C. By operating the ASIC at its maximum temperature of 125 °C, this would lead to a drift of 585 µV (1.17 V/ 10^6 • 100 °C • 5 ppm/°C). To determine the influence of this drift would require a more detailed analysis.

The AD7745 states an ENOB of 21 Bit, so the question is what resolution do you need?

BR

[3] https://ieeexplore.ieee.org/document/7969853
[5] https://www.ti.com/lit/an/slyt438/slyt438.pdf

#### _pA89

##### Junior Member level 1
Hi, thanks for detailed response
To determine the influence of this drift would require a more detailed analysis.
That -detailed analysis- could shed some light into internal operation of AD7745 IC.
The AD7745 states an ENOB of 21 Bit, so the question is what resolution do you need?
Interested in Accuracy of AD7745 when Device is Scaled - Not Mentioned in Datasheet. (e.g. Resistors can be scaled Linearly - Connecting them in Series, Non-Linearly - Connecting them in Parallel, to bring their value within range of interest)

#### stenzer

Hi,

Interested in Accuracy of AD7745 when Device is Scaled - Not Mentioned in Datasheet. (e.g. Resistors can be scaled Linearly - Connecting them in Series, Non-Linearly - Connecting them in Parallel, to bring their value within range of interest)
Sorry, I do not get the non-linear parallel configuration of the resistors. Are you talking about the TCR? If so this also affects the series configuration of resistors. Further, the TCR is usually stated with $\pm$, so it also might happen that two resistors in series or parallel might compensate each other as one might show a temperature dependent resistance increase and the other one a decrease. If you are conserned about the TCR, use one with a low ppm/°C and estimate its influence on the excitation signal amplitude. Use thin film resistors, as these show good TCR linearity and low noise, further they are available with a low (initial) tolerance.

The AD7745 has its stated accuracy of 4 aF (21 Bit ENOB). So you are interested how this accuracy is affected by your range extension circuitry. You might use a calibration structure enabling a known capacitance (Cref) to e.g. operate the AD7745 for your calibration in differential mode, and than in single ended mode. As off-the shelf capacitors usually have high tolerances you might have to create a reference capacitor by your self. E.g. if your sensor (Cx) is created as a double meander structure on a FR4 PCB, also create a reference capacitor on this PCB which can be read out without the extension circuit (low capacitance). You also might consider the AD7746 to oberate Cx and Cref in single ended mode.

BR

#### _pA89

##### Junior Member level 1
Hi,
"You might use a calibration structure enabling..."
Can we Safely Assume AD7745 also employs similar Mechanisms of MAS6510 (So that we can do Accuracy Calculations Theoretically), Equation Given Below for MAS6510 sheds some light for that IC.

[3] Capacitance to Digital Converter Based Parallelized Multi-Channel Measurement System--- https://sci-hub.do/https://ieeexplore.ieee.org/document/7969853

#### stenzer

Hi,

1) please share your considerations here in the forum instead of sending a private massage. Otherwise the conversation leads towards two different directions. And more important, also other members and visitors may benefit and contribute.
2) regarding your considerations #1: yes you may use an additional series capacitor as it decreases your sensor capacitance (two capacitors in serie). But be aware that an off-the-shelf capacitor has quite a large tolerance. So without an appropriate measurement strategy i.e. calibration, acurracy disussions make no sense.
3) regarding consideration #2: if you but a resistor in parallel to your unknow resistor than its a non-linera relation. But that isn't how you described your setup before. It seemed you talked about the range extenssion circuit, which would only change the excitatin signal amplitude, thus still resulting in an linear result when changing the sensor value (two constant resistors in parallel).

- For me it is still not clear what are you trying to achive!?
- Is your sensor a capacitive one or as intended in the PM a resistive one?
- If it is a resistive one, why using a CDC?
- How does your setup look like?
- Which accuracy is required?
- Bulk capacitance?
- Sensor change ($\Delta$C).

BR

#### _pA89

##### Junior Member level 1
Hi,
I thought it would be irrelevant to main conversation and the image shared is not edible for public in general!
For me it is still not clear what are you trying to achive!?
Exactly what is described in Pg-3 of AN-1585 - Application Note -Characteristics of Capacitive Humidity Sensor
(Also Pg-2 of CN-0346 for Better Understanding)

#### stenzer

So if yor application is identical to the example given by ADI in AN-1585 there is no need for further discussion.

The error caused by the extension circuit is ~ ±0.5%. And as it is independent of the bulk capacitance they recommend a software compensation.

As you still do not disclose how your actual setup looks like (especially the sensor topology), I'm not able to give any recommendations. There are several possible solutions to perform this compensation e.g.

- model based approach including an offset gain calibration
- or as already mentioned enabling a differential measuremnt for calibration only
- use the AD7746 which allows to create a single ended calibration “structure“, so basically you are able to perform a single ended measurement of your sensor including the extension circuit and e.g. a second channel including a second identical extension circuit and a capacitance (resistor) mapping the maximum sensor value. As the maximum error occures for the maximum sensor reading.

BR

#### _pA89

##### Junior Member level 1
Hi,
The error caused by the extension circuit is ~ ±0.5%.
Citation needed.
As you still do not disclose how your actual setup looks like
Exactly as described in CN-0346 (~ AN-1585) - Circuit Note, with P14-W from iST being Capacitive Humidity Sensor