461
edits
Changes
Jump to navigation
Jump to search
Line 180:
Line 180: − + − + − + − + − + − +
no edit summary
Another characteristic equation of transistors is
Another characteristic equation of transistors is
: <math>Z \!\cdot\! I_b = IS \!\cdot\! \exp \left( \frac{V_{be}}{V_0} \right)</math>.
: <math>Z \!\cdot\! I_b = IS \!\cdot\! \exp \left( \frac{V_{be}}{V_0} \right)\,\!</math>.
This equation is linearized by performing a Taylor expansion up to the first degree, which gives
This equation is linearized by performing a Taylor expansion up to the first degree, which gives
: <math>Z \!\cdot\! I_b = Q \!\cdot\! (V_0 + V_{be} - U)</math>.
: <math>Z \!\cdot\! I_b = Q \!\cdot\! (V_0 + V_{be} - U)\,\!</math>.
Under AC conditions this equation is modified by defining <math>V_0 = U</math>. There is one such equation for each transistor
Under AC conditions this equation is modified by defining V<sub>0</sub> = U. There is one such equation for each transistor
* <math>T_1</math>: <math>Z_1 \!\cdot\! j_b = Q_1 \!\cdot\! (V_{01} + V_3 - U_1)</math>
* T<sub>1</sub>: Z<sub>1</sub>j<sub>b</sub> = Q<sub>1</sub>(V<sub>01</sub> + V<sub>3</sub> - U<sub>1</sub>)
* <math>T_2</math>: <math>Z_2 \!\cdot\! k_b = Q_2 \!\cdot\! (V_{02} + V_7 - V_4 - U_2)</math>
* T<sub>2</sub>: Z<sub>2</sub>k<sub>b</sub> = Q<sub>2</sub>(V<sub>02</sub> + V<sub>7</sub> - V<sub>4</sub> - U<sub>2</sub>)
== Solution ==
== Solution ==
The solution (that is, <math>V_{out}</math>) is found by first iterating as described above to find the transistor operating points to the desired precision, then solving under AC conditions to find the correct <math>V_{out}</math>. "Solving" (both during iteration and for the final answer) involves running the 24-equation matrix through MATLAB and selecting out the solution generated for the <math>V_{out}</math> variable. For responses, see the article on the [[SiPM Amplifier]].
The solution (that is, V<sub>out</sub>) is found by first iterating as described above to find the transistor operating points to the desired precision, then solving under AC conditions to find the correct V<sub>out</sub>. "Solving" (both during iteration and for the final answer) involves running the 24-equation matrix through MATLAB and selecting out the solution generated for the V<sub>out</sub> variable. For responses, see the article on the [[SiPM Amplifier]].