# Charge injection Charge in the MOS of an ADC can cause issues. When turned on, a channel forms. When sampling finishes, the input and capacitor voltag will be the same. The charge stored in the channel comes from the parallel plate capacitance, the oxide capacitance (per unit area) tims the gate areaq, then multiplied by the effective voltage that formed it. This charge is negative for an n-channel transistor (positive voltage on the gate). When the clock decreases, the charge needs to be flushed out. It is assumed that half will go to the input and half will go to the capacitor, changing its voltage.   This is called charge injection. ## Gate-drain Capacitance (aka clock feedthrough) The overlap capacitance between gate and drain (Cgd in saturation) will cause a further error in the sampled value.  We can ignore CovW as it is much smaller than CH. ## Overall Error Assuming Vdd and 0V for clk, the error becomes:  We have the threshold voltage sitting there. But we can write the threshold votlage differently using the fact that the bulk is lowest voltage connected (for nmos).  This means there is a **non-linear dependency of the error upon the input voltage**. Non-linearity is very hard to correct for (unlike offset or gain error). ## Addressing Issues with Charge Injection ### Dummy Switch   Choose 1/2W for dummy switch so it soaks up half the charge from each side. Could reduce charge injection to 10%. Need to turn off the main switch first else the dummy switch's charge might come from the input source. This doesn't compensate for anything. ## Sample Switch Size Dimensions are very important! When on (charging time) - ON resistance is small signal resistance of the triode region of the transistor.  Thus the time to charge depends on the time constant  This time constant changes with Vin, so we must choose a max Vin else the time constant is too long. It would take infinitely long to charge to the threshold voltage. Small channel length and wide transistor. Keep in mind the time taken to charge and the sample error are not uncorrelated. The inverse delay error product is:  Producing:  Tradeoff: fast sampling, cop a large error. Small error, long time. Choose a channel length as small as we can, nothing else that we can do. Choose the min channel length (anything but is a poor design decision). [^1] --- # References [^1]: [vr-4602-wk06-sc02-chargeinjection](../../Spaces/University/ELEC4602%20–%20Microelectronics%20Design%20and%20Technology/Lectures/W5/vr-4602-wk06-sc02-chargeinjection.mp4)