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Chapter 16: Problem 41

A particular IC chip can dissipate \(3 \mathrm{~W}\) and contains 10 million CMOS inverters. Each inverter is being switched at a frequency \(f\). (a) Determine the average power that each inverter can dissipate without exceeding the totalallowed power. (b) If the switching frequency is \(f=5 \mathrm{MHz}\), what is the maximum capacitive load on each inverter if (i) \(V_{D D}=5 \mathrm{~V}\), (ii) \(V_{D D}=3.3 \mathrm{~V}\), and (iii) \(V_{D D}=1.5 \mathrm{~V}\).

Short Answer

Expert verified
(a) Each inverter can dissipate 0.3 碌W. (b) Maximum loads: (i) 4.8 fF, (ii) 11 fF, (iii) 53.3 fF.

Step by step solution

01

Calculate the Average Power per Inverter

The total power dissipation for all inverters is given as \(3 \text{ W}\). Since there are 10 million inverters, the average power per inverter, \(P_{avg}\), is calculated by: \[ P_{avg} = \frac{3 \text{ W}}{10^7} = 3 \times 10^{-7} \text{ W} = 0.3 \text{ 碌W} \] This is the power each inverter can dissipate on average.
02

Use Power Formula for a CMOS Inverter

The power dissipated by a CMOS inverter is given by the formula \(P = \frac{1}{2} \cdot C_L \cdot V_{DD}^2 \cdot f\), where \(C_L\) is the capacitive load, \(V_{DD}\) is the supply voltage, and \(f\) is the frequency. We're tasked with finding \(C_L\) when \(f = 5 \text{ MHz}\).
03

Calculate Maximum Capacitive Load for Case (i) \(V_{DD} = 5 \text{ V}\)

Substitute \(P_{avg} = 0.3 \text{ 碌W}\), \(V_{DD} = 5 \text{ V}\), and \(f = 5 \times 10^6 \text{ Hz}\) into the power formula: \[ 0.3 \times 10^{-6} = \frac{1}{2} \cdot C_L \cdot (5)^2 \cdot 5 \times 10^6 \] Solve for \(C_L\): \[ C_L = \frac{0.3 \times 10^{-6}}{\frac{1}{2} \cdot 25 \cdot 5 \times 10^6} = 4.8 \times 10^{-15} \text{ F} = 4.8 \text{ fF} \]
04

Calculate Maximum Capacitive Load for Case (ii) \(V_{DD} = 3.3 \text{ V}\)

Substitute \(V_{DD} = 3.3 \text{ V}\) into the power formula: \[ 0.3 \times 10^{-6} = \frac{1}{2} \cdot C_L \cdot (3.3)^2 \cdot 5 \times 10^6 \] Solve for \(C_L\): \[ C_L = \frac{0.3 \times 10^{-6}}{\frac{1}{2} \cdot 10.89 \cdot 5 \times 10^6} \approx 11 \times 10^{-15} \text{ F} = 11 \text{ fF} \]
05

Calculate Maximum Capacitive Load for Case (iii) \(V_{DD} = 1.5 \text{ V}\)

Substitute \(V_{DD} = 1.5 \text{ V}\) into the power formula: \[ 0.3 \times 10^{-6} = \frac{1}{2} \cdot C_L \cdot (1.5)^2 \cdot 5 \times 10^6 \] Solve for \(C_L\): \[ C_L = \frac{0.3 \times 10^{-6}}{\frac{1}{2} \cdot 2.25 \cdot 5 \times 10^6} = 53.3 \times 10^{-15} \text{ F} = 53.3 \text{ fF} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Average Power Calculation
In the context of CMOS inverters, average power calculation is a basic yet crucial aspect. The total power dissipation is spread across all the inverters within an IC chip. Knowing how to calculate the average power each inverter can dissipate is essential for ensuring efficient functioning.

For example, if an IC chip can dissipate 3 watts and contains 10 million CMOS inverters, the average power per inverter can be calculated using the formula:
  • Divide the total power dissipation by the number of inverters.
  • So, in this case, it is \(3 \text{ W} \div 10^7 = 3 \times 10^{-7} \text{ W} \).
  • This means each inverter can handle an average of \(0.3 \text{ 碌W}\).
Understanding this calculation helps in designing circuits that stay within power limits, avoiding overheating and possible damage.
Capacitive Load Calculation
Determining the maximum capacitive load for each CMOS inverter is another key element. This is particularly relevant when the switching frequency and supply voltage are known.

The capacitive load calculation relies on understanding the impact of the given switching frequency and supply voltage. The power formula used is:
  • \(P = \frac{1}{2} \cdot C_L \cdot V_{DD}^2 \cdot f\)
  • Where \(C_L\) is the capacitive load, \(V_{DD}\) is the supply voltage, and \(f\) is the frequency.
By substituting the known values into the formula, you can determine the maximum capacitive load that will keep power dissipation within acceptable limits. Several calculations, like those with varying supply voltages, exemplify this process, showing that changes in supply voltage affect the capacitive load significantly.
Power Dissipation Formula
The fundamental power dissipation formula for a CMOS inverter is used to understand how various factors affect power usage in circuits.

The formula is as follows:
  • \(P = \frac{1}{2} \cdot C_L \cdot V_{DD}^2 \cdot f\)
This equation takes into account:
  • The capacitive load \(C_L\).
  • The square of the supply voltage \(V_{DD}\).
  • The frequency \(f\), or how often the inverter switches states.
Each component in this equation plays a role in how much power the inverter will ultimately dissipate. By managing these components, engineers can control the power dissipation of CMOS inverters, aiding in energy efficiency and the prevention of thermal overload.
CMOS Technology
CMOS technology is widely used in constructing integrated circuits, offering distinct advantages in terms of power efficiency.

The abbreviation CMOS stands for Complementary Metal-Oxide-Semiconductor. This technology is favored mainly because:
  • It provides low static power consumption.
  • Only consumes significant power when switching states.
  • It includes both NMOS and PMOS transistors, which help in canceling out power-consuming leakage currents.
CMOS technology is crucial for modern electronics, allowing for compact, energy-efficient devices such as smartphones and computers. Knowing how power dissipation works in CMOS inverters ensures reliable and powerful circuit design.
Supply Voltage Impact
The supply voltage, often denoted as \(V_{DD}\), is critical in power dissipation for CMOS inverters because it directly influences the amount of power consumed.

Understanding the impact of supply voltage reveals crucial insights:
  • Higher supply voltages result in higher power dissipation since the power is proportional to the square of the voltage \(V_{DD}^2\).
  • Reducing the voltage helps minimize power usage, beneficial for battery-powered devices.
  • However, decreasing \(V_{DD}\) too much may lead to slower circuit performance and reduced noise margins.
Engineers often have to balance power efficiency with performance demands, which is why understanding supply voltage impact is essential for optimal circuit design.

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Most popular questions from this chapter

An analog signal in the range 0 to \(5 \mathrm{~V}\) is to be converted to a digital signal with a quantization error of less than one percent. (a) What is the required number of bits? (b) What input voltage value represents 1 LSB? (c) What digital output represents an input voltage of \(3.5424 \mathrm{~V}\) ?

Design a classic CMOS logic circuit that will implement the logic function \(Y=A \cdot(B+C)+D \cdot E\).

(a) Given inputs \(A, B, C, \bar{A}, \bar{B}\), and \(\bar{C}\), design a CMOS circuit to implement the logic function \(Y=A \bar{B} \bar{C}+\bar{A} \bar{B} C+\bar{A} B \bar{C}\). The design should not include a CMOS inverter at the output. (b) For \(k_{n}^{\prime}=2 k_{p}^{\prime}\), size the transistors in the design to provide equal switching times equal to the basic CMOS inverter with \((W / L)_{n}=1\) and \((W / L)_{p}=2\).

(a) A CMOS digital logic circuit contains the equivalent of 4 million CMOS inverters and is biased at \(V_{D D}=1.8 \mathrm{~V}\). The equivalent load capacitance of each inverter is \(0.12 \mathrm{pF}\) and each inverter is switching at \(150 \mathrm{MHz}\). Determine the total average power dissipated in the circuit. (b) If the switching frequency is doubled, but the total power dissipation is to remain the same with the same load capacitance, determine the required bias voltage.

Using a computer simulation, investigate the propagation delay time and switching characteristics of a CMOS inverter by setting up a series of CMOS inverters in cascade. Use standard transistors and assume effective \(C_{T}\) load capacitances of \(0.05 \mathrm{pF}\). Determine the propagation delay time as a function of various transistor width-to-length ratios.
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