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chapter5_ex

# chapter5_ex - CHAPTER 5 THE CMOS INVERTER Quantification of...

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180 C H A P T E R 5 T H E C M O S I N V E R T E R Quantification of integrity, performance, and energy metrics of an inverter Optimization of an inverter design 5.1 Exercises and Design Problems 5.2 The Static CMOS Inverter — An Intuitive Perspective 5.3 Evaluating the Robustness of the CMOS Inverter: The Static Behavior 5.3.1 Switching Threshold 5.3.2 Noise Margins 5.3.3 Robustness Revisited 5.4 Performance of CMOS Inverter: The Dynamic Behavior 5.4.1 Computing the Capacitances 5.4.2 Propagation Delay: First-Order Analysis 5.4.3 Propagation Delay from a Design Perspective 5.5 Power, Energy, and Energy-Delay 5.5.1 Dynamic Power Consumption 5.5.2 Static Consumption 5.5.3 Putting It All Together 5.5.4 Analyzing Power Consumption Using SPICE 5.6 Perspective: Technology Scaling and its Impact on the Inverter Metrics

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Section 5.1 Exercises and Design Problems 181 5.1 Exercises and Design Problems 1. [M, SPICE, 3.3.2] The layout of a static CMOS inverter is given in Figure 5.1. ( λ = 0.125 μm). a. Determine the sizes of the NMOS and PMOS transistors. b. Plot the VTC (using HSPICE) and derive its parameters ( V OH , V OL , V M , V IH , and V IL ). c. Is the VTC affected when the output of the gates is connected to the inputs of 4 similar gates?. d. Resize the inverter to achieve a switching threshold of approximately 0.75 V. Do not lay- out the new inverter, use HSPICE for your simulations. How are the noise margins affected by this modification? 2. Figure 5.2 shows a piecewise linear approximation for the VTC. The transition region is approximated by a straight line with a slope equal to the inverter gain at V M . The intersection of this line with the V OH and the V OL lines defines V IH and V IL . a. The noise margins of a CMOS inverter are highly dependent on the sizing ratio, r = k p / k n , of the NMOS and PMOS transistors. Use HSPICE with V Tn = | V Tp | to determine the value of r that results in equal noise margins? Give a qualitative explanation. b. Section 5.3.2 of the text uses this piecewise linear approximation to derive simplified expressions for NM H and NM L in terms of the inverter gain. The derivation of the gain is based on the assumption that both the NMOS and the PMOS devices are velocity saturated at V M . For what range of r is this assumption valid? What is the resulting range of V M ? c. Derive expressions for the inverter gain at V M for the cases when the sizing ratio is just above and just below the limits of the range where both devices are velocity saturated. What are the operating regions of the NMOS and the PMOS for each case? Consider the effect of channel-length modulation by using the following expression for the small-signal resistance in the saturation region: r o,sat = 1/ I D ). Figure 5.1 CMOS inverter layout. In Out GND V DD = 2.5 V. Poly Metal1 NMOS PMOS Poly Metal1 2 λ
182 THE CMOS INVERTER Chapter 5 3. [M, SPICE, 3.3.2] Figure 5.3 shows an NMOS inverter with resistive load.

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