ELEC

# 1127 without the biasing circuitry the idea is to

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trated in Fig. 11.27 (without the biasing circuitry), the idea is to inject a sinusoidal current into in V in in C out I I ac GND in V in in C out I I ac GND Q 1 M 1 Figure 11.27 Conceptual setup for measurement of of transistors. the base or gate and measure the resulting collector or drain current while the input frequency, , is increased. We note that, as increases, the input capacitance of the device lowers the input impedance, , and hence the input voltage and the output current. We neglect and here (but take them into account in Problem 26). For the bipolar device in Fig. 11.27(a), (11.43) Since , (11.44) (11.45) At the transit frequency, , the magnitude of the current gain falls to unity: (11.46) (11.47) That is, (11.48) The transit frequency of MOSFETs is obtained in a similar fashion. We therefore write: (11.49) Note that the collector-substrate or drain-bulk capacitance does not affect owing to the ac ground established at the output. Modern bipolar and MOS transistors boast ’s above 100 GHz. Of course, the speed of complex circuits using such devices is quite lower. Example 11.14 The minimum channel length of MOSFETs has been scaled from 1 m in the late 1980s to 65 nm today. Also, the inevitable reduction of the supply voltage has reduced the gate-source overdive voltage from about 400 mV to 100 mV. By what factor has the of MOSFETs increased?

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 557 (1) Sec. 11.3 Analysis Procedure 557 Solution It can proved (Problem 28) that (11.50) Thus, the transit frequency has increased by approximately a factor of 59. For example, if cm (V s), then 65-nm devices having an overdrive of 100 mV exhibit an of 226 GHz. Exercise Determine the if the channel length is scaled down to 45 nm but the mobility degrades to 300 cm (V s). 11.3 Analysis Procedure We have thus far seen a number of concepts and tools that help us study the frequency response of circuits. Specifically, we have observed that: The frequency response refers to the magnitude of the transfer function of a system. Bode’s approximation simplifies the task of plotting the frequency response if the poles and zeros are known. In many cases, it is possible to associate a pole with each node in the signal path. Miller’s theorem proves helpful in decomposing floating capacitors into grounded elements. Bipolar and MOS devices exhibit various capacitances that limit the speed of circuits. In order to methodically analyze the frequency response of various circuits, we prescribe the following steps: 1. Determine which capacitors impact the low-frequency region of the response and compute the low-frequency cut-off. In this calculation, the transistor capacitances can be neglected as they typically impact only the high-frequency region. 2. Calculate the midband gain by replacing the above capacitors with short circuits while still neglecting the transistor capacitances.
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