This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Introduction to Microelectronics Chapter 7 F REQUENCY A NALYSIS FOR F IRSTO RDER C IRCUITS 7.1 From Quasistatic to SingleTimeConstant Circuits Up to now we have only considered the quasistatic behavior of the transistor circuit. That is, the transistors are SO fast that they can reach steady state for the time period of interest or sampling. In this chapter, we would like to derive the lower bound in time (or upper bound in frequency) where this approximation remains valid. Since the circuit module we have considered until now is rather small, the time delay is basically caused by the RC (resistor capacitor) effect, because the inductance or the transmission line effect is negligible in small circuit modules. Our goal is to match the smallsignal amplifier circuit to a lowpassfilterlike transfer function where there is only the single time constant (STC) (called the dominant pole ) that governs the deviation from the quasistatic characteristics. As shown in Fig. 7.1, although there are many other useful frequency responses from filter or bandpass circuits, the amplifier circuits in consideration will only be mapped to the lowpass response in Fig. 7.1(a). Conventionally, the amplification factor is expressed in unit of dB (decibel): A (unitless) 20 log 10 A (dB) (7.1) The use of log is to convert multiplication of cascading amplifiers of A 1 A 2 to log 10 A 1 + log 10 A 2 , and the number 20 is arbitrarily chosen in the early days to give enough precision by using integers only. A few convenient numbers to remember: A = 1 = 0dB; A = 2 = 3dB; A = 2 = 6dB; A = 10 = 20dB; A = 100 = 40dB; A = =  6dB; A = 0.1 =  20dB. Fig. 7.1. Frequency responses of an amplified (a) lowpass; (b) highpass; (c) bandpass networks. For the amplified lowpass network in Fig. 7.1(a), we denote the corner frequency f C (or Edwin C. Kan Page 71 3/26/2010 A (dB) f (Hz) f C f T (a) A (dB) f (Hz) (b) A (dB) f (Hz) (c) A A v in v out v in v out Introduction to Microelectronics called knee frequency) as when A decreases 3dB. For frequency below f C , we can assume that the circuit has quasistatic behavior, although we need to be a bit more conservative if phase of a sinusoidal input is considered. This point will be clear in the next section. We will first examine the capacitance from the physical aspects of the transistors, and build these capacitors into the smallsignal transistor models. We will then obtain the transfer function of the singlestage amplifiers to estimate their dominant poles and corner frequency. 7.2 Capacitance in MOSFET The cross section of a pair of adjacent PMOS and NMOS transistors are shown in Fig. 7.2 as an illustration. Different technologies may have rather different geometry, such as deep trench isolation trench instead of shallow trench isolation, twinwell instead of nwell, and the substrate is replaced by silicon on insulator (SOI). Here, the NMOSFET is sitting on the p substrate, and PMOSFET is sitting within an n well. substrate, and PMOSFET is sitting within an n well....
View
Full
Document
This note was uploaded on 03/26/2010 for the course ECE 3150 taught by Professor Spencer during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 SPENCER
 Microelectronics

Click to edit the document details