# Calculation for Resistor in Phototransistor Emitter

I decided to ask here for help, I am still new at electronics, I have been trying to figure out the definitions and graphs of this phototransistor, the PT1302 (datasheet here), my doubt is how can I calculate the value of a resistor below the emitter, the $$\V_\text{out}\$$ is connected to an Op-Amp, (from which I have successfully calculated all the resistors and values for components). From what I read, the given formula for the resistor in this particular arrangement is:

I know that the $$\0.6V\$$ correspond to the $$\V_\text{CE}\$$/$$\V_\text{CEO}\$$ in the datasheet, but I don't know if I am missing a formula to calculate Ic or the current or gain through collector to emitter.

And here is the matter, how can I compute $$\R_1\$$ or $$\I_\text{C}\$$ for the formula?.

if I am not wrong $$\R_1\$$ is $$R_1=\frac{V_\text{CC}-V_\text{CE}}{I_\text{C}}. \label{1}\tag{1}$$ I would really appreciate any feedback, comment, observation or example.

If the phototransistor is used as a switch, i.e. you do not want to use it for measuring the incident light intensity, then the right way to dimension the value of $$\R_1\$$ is to choose arbitrarily a maximum collector current $$\I_\text{C}\$$ (to say the truth, the choice is not entirely arbitrary: I'll give some detail on this in the notes), read from the datasheet what is the maximum value of $$\V_\text{CE}=V_{\text{CE}_\text{(sat)}}\$$ and then use formula \eqref{1} in the form $$R_1=\frac{V_\text{CC}-V_{\text{CE}_\text{(sat)}}}{I_\text{C}}$$
Some notes on the "abitrary" choice of $$\I_\text{C}\$$.
• While from the theoretical point of view the choice of $$\I_\text{C}\$$ is entirely arbitrary, from the practical point of view there are some limits. The most notable one is the maximum admissible value for this current, found in the "Absolute Maximum Ratings" table of the datasheet. For the device you are using, this is $$\20\text{mA}\$$: however, if you want to use it as a switch i.e. if you want to have $$\V_\text{E}= V_\text{CC}-V_{\text{CE}_\text{(sat)}}\$$ even at the lowest levels of incident radiation intensity, you should choose a far lower value: for example $$\I_\text{C}\simeq 100\mu\text{A}\$$ can be a good choice.
• On the use as a "linear" radiation detector: if you are using the device for a linear application i.e. to measure light intensity, then the chosen value for $$\{I_\text{C}}\$$ should be a half of the maximum collector current allowable by the power dissipation limits of the device. this is due to the fact that in such a way, you enhance the dynamic range of the output of the device.