When
you look at data sheets for operational amplifiers you'll notice specifications
for input noise voltage and input noise current expressed in units of nV/vHz
(nanovolts per root Hertz) or as pA/vHz. At first glance, the vHz denominator
seems odd. After all, how can vHz have any physical meaning?
First,
the nV/vHz spec refers to thermal noise, or Johnson noise, caused by the effect
of temperature on the electrons in a resistive device, which pretty much
includes everything. Second, the spec identifies the spectral density of
noise as a root-mean-square (rms) value over a given bandwidth.
Say
you have a Texas Instruments OP27A op-amp with an input noise voltage (Vn)
of 3.5 nV/vHz. You'll operate the op-amp from 1,000 Hz to 20 kHz, so you take
the square root of the 19 kHz bandwidth (138 vHz). Multiply 3.5 nV/vHz by 138
vHz and you get 482 nV. If you operate the op-amp with a gain of 25, the noise
gets multiplied by 25 also, so you have 12.1 µV. Use a 1V output (0 dBV) from
the op-amp and you calculate the signal-to-noise ratio: SNR = 20 * log (1V /
12.1*10-6V) = 98 dB. (See For More Information, below)
Op-amp
data sheets might include graphs of nV/vHz versus supply voltage, ambient temperature,
source resistance and other variables. You can use this information to refine
noise calculations based on your requirements.
But
how does the vHz unit get into a noise value in the first place? In 1928, John
B. Johnson at Bell Telephone Labs explained the creation of noise in conductors
and Harry Nyquist, also at Bell Labs, followed with a paper (worth reading)
that provided a theoretical basis for this noise and related it to temperature
and resistance alone.
Engineers
often rewrite Nyquist's equation for thermal electromotive force:
E2dv =
4kRTdv as E2
= 4kRT or as E = v4kRT
Where:
k = Boltzman's constant in joules/Kelvin, R = resistance in ohms, T =
temperature in Kelvin, and E represents the noise voltage. If you write the E2
equation with k, R and T in MKS units, and drop the unit-less 4, you obtain
Equation 1.
In
Equation 2, the Kelvin units cancel out, the Amperes (A) separate, and
multiplying by s/s yields Equation 3. The (kg•m2)/(A•s3)
unit equals volts (V), so:
E2
= (V2•s) = V2 / (1/s),
E
= V / v1/s) and 1/s = Hz, so
E
= V/vHz
These
steps show the source of the V/vHz unit and that it has a empirical and
theoretical origin. Keep in mind other sources can contribute noise, too.
We looked at a number of sources to determine this year's greenest cars, from KBB to automotive trade magazines to environmental organizations. These 14 cars emerged as being great at either stretching fuel or reducing carbon footprint.
Researchers at MIT and Sandia National Labs have observed a reaction in lithium-air batteries that could help improve the design of these cells for electric vehicles and other applications.
Healthcare might seem to be an unlikely target application for the Internet of Things technology, but recent developments show small ways that big-data is going to make an impact on patient care moving into the future.
From Dell / Intel® New Paradigms in Design Work Scott Hamilton, vertical market strategist for Dell Precision workstations, 5/2/2013 3
Early in my career, I worked as a draftsman and remember the days of drawing on vellum with numbered pencils and Mylar with plastic lead. This was a fun experience in the sense that I ...
I've been using workstations for more than 10 years and love finding ways to get more performance from my system. With demanding professional applications that require more power each ...
A lasting memory from my first job as an engineer in an auto assembly plant is standing on hard concrete at six in the morning, vending-machine coffee clutched in hand, listening to ...
A quick look into the merger of two powerhouse 3D printing OEMs and the new leader in rapid prototyping solutions, Stratasys. The industrial revolution is now led by 3D printing and engineers are given the opportunity to fully maximize their design capabilities, reduce their time-to-market and functionally test prototypes cheaper, faster and easier. Bruce Bradshaw, Director of Marketing in North America, will explore the large product offering and variety of materials that will help CAD designers articulate their product design with actual, physical prototypes. This broadcast will dive deep into technical information including application specific stories from real world customers and their experiences with 3D printing. 3D Printing is
To save this item to your list of favorite Design News content so you can find it later in your Profile page, click the "Save It" button next to the item.
If you found this interesting or useful, please use the links to the services below to share it with other readers. You will need a free account with each service to share an item via that service.
Tweet This
3 
