projects:electronics:weller:wxp80_reverse_engineer:analog_measurements
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| projects:electronics:weller:wxp80_reverse_engineer:analog_measurements [2018/05/12 23:21] – admin | projects:electronics:weller:wxp80_reverse_engineer:analog_measurements [2018/05/15 00:39] (current) – [WXP80 analog measurements] admin | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== WXP80 analog measurements ====== | ====== WXP80 analog measurements ====== | ||
| - | This page shows the analog measurements of the WXP80 heating element connected to an operation | + | This page shows the analog measurements of the WXP80 heating element connected to an operational |
| ===== PTC resistance and voltages WXP80 ===== | ===== PTC resistance and voltages WXP80 ===== | ||
| Line 30: | Line 30: | ||
| \\ | \\ | ||
| - | Since the is linear, we can find a first order formula which approaches the data pretty well. A general function looks like: | + | Based on the observations we assume that the relationship between temperature and resistance |
| $R = aT + b \tag{1}$\\ | $R = aT + b \tag{1}$\\ | ||
| - | where a is the slope and b the intercept of the vertical-axis. | + | where $\begin{align*}a\end{align*}$ |
| - | A formula to calculate | + | The so called normal equations for the estimated |
| + | $$\begin{align*}n\ a + ST\ b = SR \end{align*}$$ | ||
| - | $a = \frac{n (\sum\limits_{i=1}^n | + | $$\begin{align*}ST\ |
| - | where n is the number of samples | + | with $\begin{align*}n\end{align*}$ the number of data\\ |
| + | $$\begin{align*}ST = \sum\limits_{i=1}^n | ||
| + | $$\begin{align*}STT = \sum\limits_{i=1}^n T_i^2 \end{align*}$$ | ||
| + | $$\begin{align*}SR = \sum\limits_{i=1}^n R_i \end{align*}$$ | ||
| + | $$\begin{align*}SRT = \sum\limits_{i=1}^n | ||
| + | with solution | ||
| + | $$\begin{align*}a= \frac{n\ SRT- SR\ ST}{n\ STT - ST^2} \end{align*}$$ | ||
| + | $$\begin{align*}b= | ||
| + | or alternatively | ||
| + | $$\begin{align*}b=\frac{STT\ SR - ST\ STR}{n\ STT - ST^2} \end{align*}$$ | ||
| - | The intercept of the vertical axis is given with following formula:\\ | + | With the data from the table above, the least squares trendline |
| - | $b = \frac{(\sum\limits_{i=1}^n T_i^2)(\sum\limits_{i=1}^n R_i) - (\sum\limits_{i=1}^n T_i)(\sum\limits_{i=1}^n T_iR_i)}{n (\sum\limits_{i=1}^n T_i^2) - (\sum\limits_{i=1}^n T_i)^2} \tag{2}$\\ | + | $R = 0.465T + 98.17 \tag{2}$\\ |
| + | where $\begin{align*}T\end{align*}$ is the temperature in °C and $\begin{align*}R\end{align*}$ the resistance of TH1 in Ω. | ||
| - | With the data from above, the so called least squares trendline results in:\\ | + | Please note that libre office calc offers an easy method to acquire this equation directly, using the 'show equation' |
| - | $R = 0.465T + 98.17 \tag{3}$\\ | + | The opamp is configured as a DC coupled non-inverting amplifier with a bias. To calculate the gain (G) and bias (Vb), we use following equations:\\ |
| - | where T is the temperature in °C and Rv the resistance of TH1 in Ω. | + | |
| - | Another method to acquire this line is using the 'show equation' | + | $G = 1 + \frac{R6}{R4 + \frac{R3 \cdot R5}{R3 + R5}} = 1 + \frac{1.0 \cdot 10^6}{33\cdot10^3 + \frac{33\cdot10^3 \cdot 47}{33\cdot10^3 + 47}} = 31.1 \tag{3}$\\ |
| + | where $\begin{align*}R3\end{align*}$ = 4.3kΩ, $\begin{align*}R4\end{align*}$ = 33.0kΩ, $\begin{align*}R5\end{align*}$ = 47Ω and $\begin{align*}R6\end{align*}$ = 1.0MΩ\\ | ||
| - | The opamp is configured as a DC coupled non-inverting amplifier | + | The bias voltage |
| - | $G = 1 + \frac{R6}{R4 + \frac{R3 \cdot R5}{R3 + R5}} = 1 + \frac{1.0 \cdot 10^6}{33\cdot10^3 + \frac{33\cdot10^3 \cdot 47}{33\cdot10^3 + 47}} = 31.1 \tag{5}$\\ | + | $V_b = V_{dd} \frac{R5}{R5 + R3} = 4.66 \frac{47}{47 + 4300} = 0.0501 \tag{4}$\\ |
| - | where R3 = 4.3kΩ, R4 = 33.0kΩ, R5 = 47Ω and R6 = 1.0MΩ\\ | + | where $\begin{align*}V_{dd}\end{align*}$ = 4.66v\\ |
| - | + | ||
| - | The bias voltage is a simply voltage divider with R3 and R5: | + | |
| - | + | ||
| - | $V_b = V_{dd} \frac{R5}{R5 + R3} = 4.66 \frac{47}{47 + 4300} = 0.0501 \tag{6}$\\ | + | |
| - | where Vdd is 4.66v\\ | + | |
| \\ | \\ | ||
| - | We now are able to calculate a transfer function using the PTC resistor value to find the opamp output voltage relative to the temperature. (Alternatively we could calculate the transfer function using the least squares method of the output voltage data in the table above.)\\ | + | We now are able to calculate a transfer function using the PTC resistor value to find the opamp output voltage relative to the temperature. (Alternatively we could calculate the transfer function using the least squares method of the output voltage data from the table above.)\\ |
| \\ | \\ | ||
| The transfer function is: | The transfer function is: | ||
| Line 70: | Line 76: | ||
| * Fluke 87 multimeter | * Fluke 87 multimeter | ||
| + | ==== References ==== | ||
| + | * [[https:// | ||
| + | * least square trendline | ||
projects/electronics/weller/wxp80_reverse_engineer/analog_measurements.1526160095.txt.gz · Last modified: 2018/05/12 23:21 by admin
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 4.0 International
