Basic electronic structures

Ramp generator

When Vcommand = VDD :

The current source made by T1, R1, R2, R3 charges C1 with a constant current $I_{r a m p_u p}$ during $T_{r a m p_u p}$ until Vramp reaches Vmax

$I_{r a m p_u p} = \frac{V_{D D} - V_{E} (T_{1})}{R_{3}} = \frac{V_{D D} - (V_{B} (T_{1}) + V_{E B} (T_{1}))}{R_{3}} = \frac{V_{D D} - (\frac{V_{D D} . R_{2}}{R_{1} + R_{2}} + V_{E B} (T_{1}))}{R_{3}}$

$S l o p e_{r a m p_u p} = \frac{Δ V}{Δ t} = \frac{I_{r a m p_u p}}{C_{1}}$

When $V_{r a m p} = V_{m a x}, V_{E C} (T_{1}) = 0 and I_{C} (T_{1}) = 0 \Rightarrow V_{m a x} = V_{B} (T_{1}) + V_{E B} (T_{1}) = \frac{\frac{V_{D D}}{R_{1}} + \frac{V_{D D} - V_{E B} (T_{1})}{R_{3}}}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}} + V_{E B} (T_{1})$

$T_{r a m p_u p} = S l o p e_{r a m p_u p} . (V_{m a x} - V_{m i n}) = \frac{I_{r a m p_u p}}{C_{1}} (V_{m a x} - V_{m i n})$

When Vcommand = GND :

The current source made of T2, R4, R5, R6 discharge C1 with a constant current $I_{r a m p_d o w n}$ during $T_{r a m p_d o w n}$ until Vramp reaches Vmin

$I_{r a m p_d o w n} = \frac{V_{E} (T_{2})}{R_{6}} = \frac{V_{B} (T_{2}) - V_{B E} (T_{2})}{R_{6}} = \frac{\frac{V_{D D} . R_{4}}{R_{4} + R_{5}} - V_{B E} (T_{2})}{R_{6}}$

$S l o p e_{r a m p_d o w n} = \frac{Δ V}{Δ t} = \frac{I_{r a m p_d o w n}}{C_{1}}$

When $V_{r a m p} = V_{m i n}, V_{C E} (T_{2}) = 0 and I_{C} (T_{2}) = 0 \Rightarrow V_{m i n} = V_{B} (T_{2}) - V_{B E} (T_{2}) = \frac{\frac{V_{D D}}{R_{5}} + \frac{V_{B E} (T_{2})}{R_{6}}}{\frac{1}{R_{4}} + \frac{1}{R_{5}} + \frac{1}{R_{6}}} - V_{B E} (T_{2})$

$T_{r a m p_d o w n} = S l o p e_{r a m p_d o w n} . (V_{m a x} - V_{m i n}) = \frac{I_{r a m p_d o w n}}{C_{1}} (V_{m a x} - V_{m i n})$