CMOS Inverter and PIXEL (photo diode plus amplifier)

In previous post Feedback CS NMOS and current mirror, large signal analysis of drain connected NMOS is discussed. Same analysis will work for diode connected PMOS also.  

Both of them can be used to generate voltage reference given by respective reference currents and transistor sizes. Now play time. What if we connect the output nodes of each circuit together? 

   The currents and voltages will be adjusted such that both transistors are in saturation and KCL are obeyed. The actual currents in the transistors depend on the difference of reference currents and in turn determines the output node voltage.

 

This is CMOS inverter with a current flowing into the device and feedback. 

 If the net reference current is positive, implies more current is flowing in NMOS than that of PMOS. If $$ \mu_{n}C_{ox}(\frac{W}{L})_{n} = \mu_{p}C_{ox}(\frac{W}{L})_{p} $$ and $$ V_{tn} = |V_{tp}| $$ then the output voltage is higher that 0.5 Vdd.                        

If the reference current is negative, then we can see more current in PMOS than that of NMOS. Then the output is less that 0.5Vdd. If the reference current is larger in magnitude the output voltage will be either VDD or 0V. 

Lets say the output voltage $V_{o} = V_{M}$ is in the vicinity of Vdd/2. What if we add a small ac current $\delta I$ in parallel to the current source? 

Say $$\delta I = i_{0} sin(\omega t) $$. The output voltage will be $$V_{o} = V_{M} + (gain) \delta i_{0} sin(\omega t) $$ where $$ gain = \frac{1}{g_{mn}} || r_{on} || \frac{1}{g_{mp}} || r_{op} $$     

If we want maximum swing just remove the reference current. Then $$ V_{M} = \frac{V_{DD}}{2}$$

In this way the circuit a transresistance/transimpedance is implemented. 

 

This is very much used in high-speed fiber-optics interconnects as transimpedance amplifier with slight modification as shown in figure 5. Standard practice is to use the channel of the MOSFET as feedback resistor.  

This is called "pixel - photo diode plus amplifier".

Variants of this are possible to improve bandwidth and noise immunity. In place of feedback resistor, a voltage follower can be inserted to isolate the gate-source capacitance from photo diode and to increase the output drive capability.