Discrete time filters (switch-capacitor filters)

o Characteristics of all active filters depend on the accuracy of their RC time constants

o Typical precision achieved for integrated resistors and capacitors is more than 10%

o Error of any RC time constant may be as large as 20%

o Ratio of capacitor values on a chip can be accurately controlled

o Switched capacitor filters use these capacitor ratios to achieve precision

Key idea of Switch-Capacitor (SC) circuits:

Shown on the case of an integrator

• Combination of C₁ and the switch S₁ simulates a resistor
• Switch S₁ toggles continuously at a clock frequency f_C
• Capacitor C₁ charges to V_in when S₁ is to the left
• Charge from C₁ is dumped into the integrator summing node when S₁ is to the right
• Charge on C₁ during each clock cycle is

• Average current transferred to the summing junction

• Same effect as a resistor of value

• Integrator cutoff frequency

• Value of w₀ can be controlled with great accuracy because the ratio of two capacitors on the same chip
  can be kept as small as 1%

• Area needed by the simulated resistor is usually much smaller than that needed for a direct realization

• Filter characteristics can be changed by changing f_C