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TSEK03: Radio
Frequency Integrated
Circuits (RFIC)
Lecture 1: Noise
Ted Johansson, ISY
[email protected]
2
Overview
• Razavi: Chapter 2.3, pp. 35-58.
• Lee: Chapter 11, pp. 334-362.
• Noise: Sources of noise, noise spectrum,
thermal noise, 1/f (flicker) noise.
• Calculations: Noise in circuits and noise
calculation, noise factor/figure, Friis' equation
for cascaded noisy circuits blocks.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
3
2.3 Noise
• What is noise? Typically, it is known as “everything
except signal”:
N(t)
X(t)
t
t
• It affects the sensitivity of communication systems
• There are different types of noise (e.g. thermal noise,
shot noise, flicker noise, etc.)
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
4
This is strictly not noise!
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
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2.3.1 Noise
• The average current remains equal to VB/R but the
instantaneous current displays random values.
Lower temperature
Higher temperature
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
6
2.3.1 Noise
• Average noise power:
• T must be long enough to accommodate several
cycles of the lowest frequency.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
7
2.3.2 Noise Spectrum
• To measure the signal’s frequency content at 10 kHz,
we need to filter out the remainder of the spectrum
and measure the average power of the 10-kHz
component.
Noise Spectrum
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
8
Power Spectral Density (PSD)
• Power Spectral Density (PSD) is the Sx(f).
• Total area under Sx(f) represents the average power
carried by x(t).
• Two-sided spectrum is scaled down vertically by
factor of 2.
Two-Sided
One-Sided
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
9
Thermal Noise
• Charge carriers, which are thermally affected
generate a random varying current. It produces a
random voltage which is called “thermal noise”.
• Thermal noise power is proportional to T [K]. The onesided PSD of a resistor is given by:
Sv(f) = 4kTR
(k=1.38E-23 J/K)
[V2/Hz]
• It is independent of frequency, because it is
considered as “white” noise (noise power is the same
over any given absolute bandwidth).
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
10
Example 2.15
A resistor of value R1 generates a noise voltage whose
one-sided PSD is given by
(a) What is the total average power carried by the noise
voltage?
(b) What is the dimension of Sv(f)?
(c) Calculate the noise voltage for a 50-Ω resistor in 1 Hz
at room temperature.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
11
Effect of Transfer Function on Noise
• Effect of a low-pass filter on white noise:
• Generally, with a transfer function H(s):
• Define PSD to allow many of the frequency-domain
operations used with deterministic signals to be applied
to random signals as well.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
12
2.3.4 Thermal Noise
• Resistor thermal noise (PSD) models:
Thevenin
Norton
• Polarity of the sources is unimportant but must be
kept same throughout the calculations
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
13
Example 2.16
• Sketch the PSD of the noise voltage measured across
the parallel RLC tank depicted in figure below.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
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Example 2.16 (cont)
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Example 2.16 (cont)
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
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Thermal Noise
• Example (homework!): Calculate the equivalent
noise voltage of two parallel and two series
resistors, R1 and R2.
• Answers:
–Parallel:
–Series:
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
17
A Theorem about Lossy Circuit
• If a passive circuit dissipates energy, then it must contain a
physical resistance and must therefore produce thermal
noise. We loosely say “lossy circuits are noisy.”
• If the real part of the impedance seen between two terminals
of a passive (reciprocal) network is equal to Re{Zout}, then
the PSD of the thermal noise seen between these terminals is
given by 4kTRe{Zout}
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
18
Noise in MOSFETs
• Thermal noise of MOS transistors operating in the
saturation region is approximated by a current source
tied between the source and drain terminals, or can
be modeled by a voltage source in series with gate.
”excess noise coefficient”, 2/3 for long channel
and up to 2 for short channel devices
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
19
Thermal Noise in MOSFETs
• The gate noise due to gate resistance:
As proved in [6]
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20
Ohms/square? square what?
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21
Thermal Noise in MOSFETs
• Good design: Gate noise much less than drain noise
• At very high frequencies thermal noise current flowing
through the channel couples to the gate capacitively,
”gate-induced noise current”
• G/S/D terminal resistance can
be reduced by parallel transistors
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
22
Flicker Noise
• Flicker noise or 1/f noise appears at low frequencies.
It increases when frequency decreases.
• Flicker noise in MOSFET
Transistor width
Gate length
• K is a process dependent constant, which is typically
lower for PMOS devices than NMOS transistors.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
23
Example 2.17
• Can the flicker noise be modeled by a current source?
• Yes, a MOSFET having a small-signal voltage source of
magnitude V1 in series with its gate is equivalent to a
device with a current source of value gmV1 tied between
drain and source.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
24
Flicker Noise: corner frequency
• For CMOS devices, the 1/f noise corner falls in the
range of tens or hundreds of MHz in today’s MOS
technologies.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
25
Noise in Bipolar Transistors
• Bipolar transistors contain physical
resistances in their base, emitter, and
collector regions, all of which generate
thermal noise. Moreover, they also suffer
from “shot noise” associated with the
transport of carriers across the baseemitter junction.
• In low-noise bipolar circuits, the base
resistance thermal noise and the collector
current shot noise become dominant. For
this reason, wide transistors biased at
high current levels are employed.
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
26
Noise Temperature
• Sometime you can see the term "Noise Temperature".
What is this?
• Definition: "the equivalent temperature of a source
impedance into a perfect (noise-free) device that would
produce the same added noise".
TN
F =1+
⇒ TN = Tref (F −1)
Tref
Tref = 290 K
• Ex:
NF=3 dB => TN = 289 K
NF=1 dB
TN = 75 K
TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson
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