Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

Switched-Capacitor Filters 17-1717.4.8 Channel Mobile ChargeCharge injection also occurs due to the mobile charge in the channel. If the transistor is biased in linearregion, the channel mobile charge can be approximated byQ ch ¼ C GS (V GS V T ) (17:45)where C GC is the gate-channel capacitor; see Figure 17.14.When the switch is turned off this charge is released and part of it goes to the sampling capacitor.Fortunately, the previously discussed early clock phase technique for the reduction of clock feedthroughalso reduces the effects of the channel mobile charge injection. The mobile charge injected to thesampling capacitor is a function of several parameters, e.g., input signal, falling rate of the clock, overlapcapacitors, gate capacitor, threshold voltage, integrating capacitor, and the supply voltages.The effects of the channel mobile charges are severe when the f 1 -driven transistor is opened before thef 0 1-driven transistor. In this case, the situation is similar to that shown in Figure 17.13a, in which oneterminal of C S is still grounded. While f 1 is higher than v i þ V T the channel resistance is small and v iabsorbs most of the channel-released charge. For f 1 < v i þ V T , the channel resistance increases furtherand a substantial amount of charge released by the channel will flow through C S , introducing a chargeerror. If the clock phases are arranged as shown in Figure 17.13b, most of the charge released by thechannel returns back to v i . The main reason is because the equivalent capacitor seen at the right-handside of the transistor is nearly equal to C p3 ,ifC p2 is neglected, making this a high-impedance node.Because this parasitic capacitor is smaller than the sampling capacitor, a small amount of extracted(or injected) charge will produce a huge variation on v y , see Figure 17.13b, pushing back most of themobile charges. Equation 17.45 shows that the mobile charge is a function of V GS (¼V clock V in for thesampling switch), hence the part of the charge injected into the sampling capacitor is signal dependent.This issue can be alleviated if the clock is correlated with the incoming signal such that VGS ismaintained constant using charge pumps circuits; the technique proposed in Ref. [14] implements thisconcept.17.4.9 Dynamic RangeThe dynamic range is defined as the ratio of the maximum signal that the circuit can drive withoutsignificant distortion to the noise level. The maximum distortion tolerated by the circuit depends on theapplication, but 60 dB is commonly used. Since the linearity of the capacitor is good enough and if theharmonic distortion components introduced by the OTA input stage are small, the major limitation forFIGURE 17.14Cross section of the MOS transistor showing the mobile charge.