CHAPTER 2

Power considerations in sub-micron digital CMOS


Prev TOC Next

2.2. Fundamental limits

Fundamental limits for power can be derived from the basic principles of electromagnetics, thermodynamics and quantum mechanics [1], [2], [3]. They are asymptotic limits and give the minimum possible power.

2.2.1. Thermodynamic limit

The thermodynamic limit can be derived from the following model. The resistor R with a mean square noise voltage given in fig.2.2 has been applied to a digital circuit modeled with an equivalent resistance R. The available noise power is PAV =kTDf (see reference [4]) where k is Boltzmann’s constant, T is absolute temperature and Df is the noise bandwidth. Since we want to transfer energy to the circuit in a digital form, the average signal power PS transferred, should be greater than the available noise power PAV by a factor g ³ 1. Therefore, the switching energy Es transferred to the digital circuit should be:

( 2.1)

Although, the constant factor g is larger than one we do not know yet how large has to

be, in order to be able to have the probability of error in data transmission sufficiently small. For comparison sake, the necessary energy to move a single electron through a potential difference of about 0.1V it is in the order of 4kT=0.1eV at room temperature.

The probability of errors due to the thermal noise can be found by using Poisson distribution and it is proportional to:

(2.2)

 

 

 

Fig.2.2: Thermodynamic limit

 

The bit error rate in a modern digital transmission BER should be better than 10-10. As a conclusion, in order to get reliable results, we have to use switching energies with a factor g=107 larger than the above mentioned value.

2.2.2. Quantum mechanics limit

The uncertainty principle derived by Heisenberg provides the second fundamental limit [5]. An energy change D E associated with a switching transition must satisfy the following condition to give a measurable outcome:

(2.3)

where D t is the switching time and h is Plank's constant. During a switching transition of a single electron wave packet, the required average power P can be deducted from (2.3) as:

(2.4)

The point where the thermodynamic limit reaches the same value as the quantum limit

represents the boundary between the region where the electron can be treated as a classical particle and the region where it must be treated as a wave packet. Hence, the switching time D t can be computed as a function of absolute temperature:

Fig.2.3: Fundamental limits of power in digital

(2.5)

Fig.2.3 illustrates the fundamental limits of power in digital signal processing from thermodynamics and quantum mechanics considerations in the power P-delay Dt plane. The value of g is taken 4 for the sake of comparison. Switching transitions at the left of their loci are forbidden. The zone for low power lies to the right of those limits.

The physical limits shown above are not the only limits where power can be addressed. Material limits, circuit limits and system limitations can bring also clues about power. The fundamental limits are asymptotic limits and show how far one can go in the direction of power reduction. For realistic comparisons between different possible implementations of the same digital function we have to address the practical limits as explained in the following section.

Rand3D

Featured Video
Jobs
Mechanical Engineer I for Air Techniques, Inc at Melville, NY
Proposal Support Coordinator for Keystone Aerial Surveys at Philadelphia, PA
Upcoming Events
The Rise of Mechatronics at Dassault Systèmes San Diego 5005 Wateridge Vista Drive San Diego CA - Sep 12, 2017
The Rise of Mechatronics at Buca di Beppo - Pasadena 80 West Green Street Pasadena CA - Sep 13, 2017
The Rise of Mechatronics at Dassault Systèmes Santa Clara 3979 Freedom Circle, Ste 750 Santa Clara CA - Sep 14, 2017
The 30th Annual Integrated Process Excellence Symposium & Training at Wyndham Grand Bonnet Creek Resort Orlando FL - Sep 18 - 20, 2017
Kenesto: 30 day trial
SolidCAM: Cutting Webinar



Internet Business Systems © 2017 Internet Business Systems, Inc.
25 North 14th Steet, Suite 710, San Jose, CA 95112
+1 (408) 882-6554 — Contact Us, or visit our other sites:
AECCafe - Architectural Design and Engineering EDACafe - Electronic Design Automation GISCafe - Geographical Information Services TechJobsCafe - Technical Jobs and Resumes ShareCG - Share Computer Graphic (CG) Animation, 3D Art and 3D Models
  Privacy Policy Advertise