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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 5 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 14 Example 2.16 (cont) TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson 15 Example 2.16 (cont) TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson 16 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] TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson 20 Ohms/square? square what? TSEK03 Integrated Radio Frequency Circuits 2017/Ted Johansson 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