Charge Injection

Charge injection is the error a sampled-data circuit inherits from the act of switching itself off: a MOSFET used as a switch stores charge in its channel while conducting, and the instant it turns off, that charge has to go somewhere — some of it dumps onto whatever capacitor the switch was just connecting, corrupting the very voltage the circuit was trying to hold steady.

The source of the error is nothing exotic — it is the switch doing exactly what it was designed to do. A MOSFET conducting as a closed switch has an inverted channel full of mobile charge carriers, with total charge Q_ch proportional to the gate overdrive and the device's own width and length. That charge is what lets current flow freely while the switch is on; it is not optional or parasitic, it is the mechanism of conduction itself. When the gate voltage falls to turn the switch off, that channel charge does not simply vanish — it has to exit through the source and drain terminals, since there is nowhere else physically connected to it.

Where that charge goes, and in what proportion, is what actually determines the error. In the idealized case the channel charge splits evenly between the source and drain terminals; in practice the split depends on how fast the gate falls and on the relative impedance each terminal presents at that instant. Whatever portion flows onto the sampling capacitor the switch was connected to adds or removes charge from a node that is supposed to be isolated and holding a fixed voltage — and since charge divided by capacitance is a voltage, that unwanted charge shows up directly as an error voltage added to whatever signal the capacitor had just finished sampling.

Charge injection is routinely confused with a second, physically distinct error that happens at the same instant — clock feedthrough. Feedthrough is pure capacitive coupling: the falling clock edge driving the switch's gate couples through the gate-to-source and gate-to-drain overlap capacitance directly onto the hold node, independent of whether the channel held any charge at all. Charge injection depends on the channel charge that was actually present; feedthrough depends only on the clock swing and the overlap capacitance geometry. Both corrupt the sampled voltage at the same moment and both are commonly reduced by the same circuit trick, which is part of why practitioners frequently lump them together as one effect even though the physics differ.

The dominant mitigation technique exploits the fact that both errors are, to first order, predictable and symmetric. A dummy transistor — typically half the width of the real switch — is placed next to it, driven by the complementary clock phase, with its source and drain tied together and connected to the signal node. When the main switch turns off and injects charge, the dummy device's own clock transition is arranged to absorb an equal and opposite charge, canceling the error to first order; because the dummy is sized at half the main switch's width, it can supply the opposite-polarity charge the main device's full channel charge would otherwise require. This cancellation is only first-order — mismatch between the two devices, and the fact that cancellation depends on both charges splitting in correlated ways, leaves a residual error that shrinks but does not vanish.

This is why practically every sample-and-hold, switched-capacitor filter, and switched-capacitor analog-to-digital converter spends real design effort on switch sizing rather than treating it as a detail. Making the switch smaller reduces both the channel charge available to inject and the overlap capacitance available for feedthrough, but a smaller switch also has higher on-resistance, which trades away settling speed and bandwidth — so switch sizing in a sampled-data circuit is a direct tradeoff between speed and this specific error source, not an independent choice either way.

Charge injection is the reminder that a switch is never truly invisible to the node it isolates — it leaves behind exactly the charge it needed to conduct in the first place. Every sampled-data circuit's accuracy floor ultimately traces back to how completely that leftover charge can be canceled, not eliminated, since the physics that makes a MOSFET a usable switch is the same physics that guarantees it leaves something behind when it turns off.