Update the sensor card expression for AMDC article (#144)

* Update the sensor card equation

* Revise voltage equations and connector details

Updated voltage equations for Revision B and C, and added details about connectors.

* Update ADC voltage references in documentation

* Document ADC voltage relationship for sensor boards

Added section explaining the relationship between input and ADC voltage for low-voltage sensor boards.

* Change header from H4 to H3 for ADC voltage section

* Update index.md

* Update index.md

* Update voltage measurement equations for revisions

* Update voltage measurement formula for Revision B

* Update index.md

* Fix link reference in ADC voltage relationship section

* Fix link formatting in ADC voltage relationship section

Updated link formatting for consistency in the documentation.

* Enhance index.md with ADC voltage equations

Added general expression for ADC voltage relationship and primary current calculation.

* Clarify ADC voltage relationship and revisions

* Fix equation formatting in index.md

* Update revision label from B to A, B

* Clarify ADC voltage relationship and revisions

Updated the relationship between measured voltage and ADC input voltage, including general expression and revisions A, B, and C.

* Revise sensor conversion ratio and resistor values

Updated sensor conversion ratio notation and clarified K_N value.

* Clarify sensor conversion ratio in documentation

* Update design parameters in index.md

* Fix redundancy in K_N notation in revisions A, B, C

* Fix voltage equation formatting in index.md

* Fix precision in voltage calculations in index.md

* Fix formatting in sensor cards index documentation

* Fix equation formatting in low-voltage index.md

* Fix reference voltage variable in equation

Corrected the reference voltage variable in the equation from 'V_{ref}' to 'V_{REF}' for consistency.

* Update index.md

* Fix reference to ADC version in calculations

* Fix formatting of PRIMARY current equation

* Clarify ADC voltage relationship terminology

Updated the terminology from 'measured voltage' to 'input voltage' for clarity.

* Clarify input voltage terminology in ADC section

Updated the terminology for input voltage in the ADC relationship section.

Author: Daehoon-Sung

source/accessories/amds/sensor-cards/current/index.md

@@ -91,26 +91,31 @@ A single-ended ADC was selected. The ADC used is the Texas Instruments [ADS8860]
 The maximum data throughput for a single chip is 1 MSPS but decreases by a factor of N for N devices in the daisy-chain. 
 The input voltage range is 0-$V_{\rm REF}$. The positive input pin of the ADC `AINP` is connected to the output of the low pass filter, and the negative input pin `AINN` is connected to `GND`.
 
-#### Final Primary Current-to-ADC Input Voltage Relationship
+#### Relationship Between Input and ADC voltage
 
-From the equations provided in the [Op Amp Stage](op-amp-stage) section, the relationship between the measured current $I_{\rm PRIMARY}$ and the input voltage of ADC $V_{\text{out}}$ can be calculated for each revision of the current sensor board as follows:
+From the equations provided in the [Op Amp Stage](#op-amp-stage) section, the general relationship between the measured current $I_{\rm PRIMARY}$ and the input voltage of ADC $V_{\text{ADC}}$ can be calculated, and the relationship for each revision of the current sensor board is provided below:
 
-##### Revision B
+##### General Expression
 
-In this design, $V_{\rm REF}$ = 5V, $R_{\rm BURDEN}$ = 150Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 8.45kΩ, $R_{\rm c}$ = 4.64kΩ, resulting in:
+$$ 
+I_{\text{PRIMARY}} = \frac{N_2}{N_1} \left[ \frac{ ( R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c} )(R_{a} + R_{\text{BURDEN}}) - R_{b} R_{c} R_{\text{BURDEN}}}{ R_{a} R_{b} R_{c} R_{\text{BURDEN}}} \right] \left[ V_{\text{ADC}} - \frac{ R_{a} R_{b} (R_{a} + R_{\text{BURDEN}}) }{ ( R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c} )(R_{a} + R_{\text{BURDEN}}) - R_{b} R_{c} R_{\text{BURDEN}}} V_{\text{REF}} \right] 
+$$
+
+##### Revision A, B
+
+In this design, _N_<sub>1</sub>:_N_<sub>2</sub> = 1:1000, $V_{\rm REF}$ = 5V, $R_{\rm BURDEN}$ = 150Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 8.45kΩ, $R_{\rm c}$ = 4.64kΩ, resulting in:
 
 $$
-V_{\text{out, RevB}} = 2.4922 + 0.034 I_{\text{PRIMARY}} \qquad { \rm [V]}
+I_{\text{PRIMARY}} = 29.2579 \times (V_{\text{ADC, RevA,B}} - 2.4922) \qquad {\rm [A]}
 $$
 
 ##### Revision C
-In this design, $V_{\rm REF}$ = 4.5V, $R_{\rm BURDEN}$ = 150Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 10.7kΩ, $R_{\rm c}$ = 4.12kΩ, resulting in:
+In this design, _N_<sub>1</sub>:_N_<sub>2</sub> = 1:1000, $V_{\rm REF}$ = 4.5V, $R_{\rm BURDEN}$ = 150Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 10.7kΩ, $R_{\rm c}$ = 4.12kΩ, resulting in:
 
 $$
-V_{\text{out, RevC}} = 2.5126 + 0.034 I_{\text{PRIMARY}} \qquad { \rm [V]}
+I_{\text{PRIMARY}} = 29.4146 \times (V_{\text{ADC, RevC}} - 2.5126) \qquad \mathrm{[A]}
 $$
 
-
 ### Connectors
 - There are two screw terminals `P5` and `P6` to connect the conductor in which the current is to be measured
 - A screw terminal block `P1` is used to connect the +-15V supply for the current sensor

source/accessories/amds/sensor-cards/high-voltage/index.md

@@ -42,10 +42,18 @@ The voltage across the burden resistor is a bipolar signal (voltage span include
 This circuit is used to translate the voltage across the burden resistor, which is bipolar, to the ADC input range of 0-4.5V. The resistor values can be calculated analytically using the following formula:
 
 $$
-V_\text{out} = \frac{R_b||R_c}{R_a + (R_b||R_c)}\times V_\text{BURDEN} + \frac{R_a||R_b}{R_c + (R_a||R_b)}\times V_\text{REF}
+V_{\rm out} = \frac{R_{\rm a} R_{\rm b}}{R_{\rm a} R_{\rm b} + R_{\rm a} R_{\rm c} + R_{\rm b} R_{\rm c}} V_{\rm REF} + \frac{R_{\rm b} R_{\rm c}}{R_{\rm a} R_{\rm b} + R_{\rm a} R_{\rm c} + R_{\rm b} R_{\rm c}} V_{\rm BURDEN}
 $$
 
-The algebra can get quite complicated when solving it analytically. So the resistor values were computed to be R<sub>a</sub> = 10kΩ, R<sub>b</sub> = 8.45kΩ, and R<sub>c</sub> = 4.64kΩ using the TI analog engineer's calculator.
+A more precise expression for $V_{\rm BURDEN}$ can be derived as:
+
+$$
+V_{\mathrm{BURDEN}} = \frac{1}{R_{\mathrm{a}} + R_{\mathrm{BURDEN}}}\left(R_{\mathrm{BURDEN}} V_{\mathrm{out}} + \frac{K_{N} R_{\mathrm{a}} R_{\mathrm{BURDEN}}}{2R_{\mathrm{IN}}} V_{\mathrm{IN}}\right)
+$$
+
+where R<sub>BURDEN</sub> is the burden resistor, R<sub>IN</sub> is the input resistance, and K<sub>N</sub> is the sensor conversion ratio from the datasheet. For LV-25P, the data sheet lists _N_<sub>1</sub>:_N_<sub>2</sub> = 2500:1000 and K<sub>N</sub> = 2.5.
+
+The algebra can get quite complicated when solving it analytically. So the resistor values were computed to be R<sub>a</sub> = 10kΩ, R<sub>b</sub> = 8.45kΩ, and R<sub>c</sub> = 4.64kΩ using the [TI analog engineer's calculator](https://www.ti.com/tool/ANALOG-ENGINEER-CALC).
 
 **Note:** As the op-amp output voltage approaches the supply rails, it tends to distort and behave nonlinearly so the output voltage is limited to actually be 0.2V to 4.5V.
 
@@ -60,16 +68,32 @@ $$
 
 ### Analog to Digital Converter
 To increase noise immunity, the card has an inbuilt Analog to Digital Conversion (ADC) IC. The ADC used is the Texas Instruments ADS8860. It is pseudo-differential input, SPI output, SAR ADC. The maximum data throughput for a single chip is 1 MSPS but decreases by a factor of N for N devices in the daisy-chain. 
+The different stages of the voltage sensor card described above convert the input voltage, to a voltage in the range of 0.2V - 4.5V. For the current design, 0V input voltage corresponds to 2.35V at the ADC input. The positive peak corresponds to 4.5V and the negative peak corresponds to 0.2V. 
+
+#### Relationship Between Input and ADC voltage
+From the equations provided in the [Level shift stage](#level-shift-stage) section, the general relationship between the input voltage $V_{\rm IN}$ and the ADC input voltage $V_{\text{ADC}}$ can be calculated, and the relationship for each revision of the current sensor board is provided below:
+
+##### General Expression
 
-The different stages of the voltage sensor card described above convert the input voltage, to a voltage in the range of 0.2V - 4.5V. The voltage at the ADC input V<sub>ADC</sub> is related to the sensor card input voltage V<sub>IN</sub> as follows:
+$$
+V_{\mathrm{IN}} = \frac{2 R_{\mathrm{IN}}\left[(R_{\mathrm{a}}R_{\mathrm{b}} + R_{\mathrm{a}}R_{\mathrm{c}} + R_{\mathrm{b}}R_{\mathrm{c}})(R_{\mathrm{a}} + R_{\mathrm{BURDEN}}) - R_{\mathrm{BURDEN}}R_{\mathrm{b}}R_{\mathrm{c}}\right]}{K_{N}R_{\mathrm{a}}R_{\mathrm{b}}R_{\mathrm{c}}R_{\mathrm{BURDEN}}}\left(V_{\mathrm{ADC}} - \frac{(R_{\mathrm{a}} + R_{\mathrm{BURDEN}})R_{\mathrm{a}}R_{\mathrm{b}}}{(R_{\mathrm{a}}R_{\mathrm{b}} + R_{\mathrm{a}}R_{\mathrm{c}} + R_{\mathrm{b}}R_{\mathrm{c}})(R_{\mathrm{a}} + R_{\mathrm{BURDEN}}) - R_{\mathrm{b}}R_{\mathrm{c}}R_{\mathrm{BURDEN}}} V_{\text{REF}} \right)
+$$
+
+##### Revision A
+
+In this design, K<sub>N</sub> = 2.5, $V_{\rm REF}$ = 5V, $R_{\rm BURDEN}$ = 390Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 8.45kΩ, $R_{\rm c}$ = 4.64kΩ, $R_{\rm IN}$ = 25kΩ, resulting in:
 
 $$
-V_\text{ADC} = \frac{R_b||R_c}{R_a+(R_b||R_c)}\left( \frac{V_\text{IN}R_\text{BURDEN}}{R_\text{IN}}K_\text{N}\right)+\frac{R_a||R_b}{R_c+(R_a||R_b)}\times V_\text{REF}
+V_{\text{IN}} = 229.1697 \times (V_{\text{ADC, RevA}} - 2.5054) \qquad {\rm [V]}
 $$
 
-where R<sub>BURDEN</sub> is the burden resistor, R<sub>IN</sub> is the input resistance, and K<sub>N</sub> is the sensor conversion ratio from the datasheet. For LV-25P, the data sheet lists K<sub>N</sub> = 2500:1000.
+##### Revision B, C
 
-For the current design, 0V input voltage corresponds to 2.35V at the ADC input. The positive peak corresponds to 4.5V and the negative peak corresponds to 0.2V.
+In this design, K<sub>N</sub> = 2.5, $V_{\rm REF}$ = 5V, $R_{\rm BURDEN}$ = 348Ω, $R_{\rm a}$ = 10kΩ, $R_{\rm b}$ = 8.45kΩ, $R_{\rm c}$ = 4.64kΩ, $R_{\rm IN}$ = 25kΩ, resulting in:
+
+$$
+V_{\text{IN}} = 256.0223 \times (V_{\text{ADC, RevB,C}} - 2.5031) \qquad {\rm [V]}
+$$
 
 ### Connectors
 - The HV terminal block `B1` with screw connectors is used to connect the HV terminals across which voltage has to be measured. 
@@ -95,4 +119,4 @@ A user may want to change some of the passive components based on the range requ
 - [Voltage sensor](https://github.com/Severson-Group/AMDS/blob/develop/HighVoltageCard/datasheets/LV25P_Sensor.pdf)
 - [Op Amp](https://github.com/Severson-Group/AMDS/blob/develop/HighVoltageCard/datasheets/OPA320_OpAmp.pdf)
 - [Voltage Reference (LDO)](https://github.com/Severson-Group/AMDS/blob/develop/HighVoltageCard/datasheets/REF5045_LDO.pdf)
-- [ADC](https://github.com/Severson-Group/AMDS/blob/develop/HighVoltageCard/datasheets/ADS_8860_ADC.pdf)
+- [ADC](https://github.com/Severson-Group/AMDS/blob/develop/HighVoltageCard/datasheets/ADS_8860_ADC.pdf)

source/accessories/amds/sensor-cards/low-voltage/index.md

@@ -24,11 +24,19 @@ Since these requirements very closely mirror the analog inputs on the AMDC, a si
 
 Various ADCs are available which are pin-compatible to the part designed into the PCB. This means that the user can select which one they want when they assemble the boards. The ADCs offer the same specs, but vary on the sample rate. More expensive ADCs provide a higher sample rate.
 
+### Relationship Between Input and ADC voltage
+
+For both REV A and REV B low-voltage sensor boards with $V_{\rm REF}$ = 2.048V, the relationship between the input voltage $V_{\rm IN}$ and the ADC input voltage $V_{\text{ADC}}$ is given by:
+
+$$
+V_{\text{IN}} = V_{\rm IN+} - V_{\rm IN-} = (V_{\text{ADC}} - 2.048) \times 10 \qquad {\rm [V]}
+$$
+
 ### Pin Compatible ADCs
 
 The default ADC is **bolded** below, but any of the follow ADCs work with the design.
 
 - 100 kSPS: ADS8867
 - **400 kSPS: ADS8865**
 - 680 kSPS: ADS8863
-- 1000 kSPS: ADS8861
+- 1000 kSPS: ADS8861