Dark Secrets of RF Design

Dark Secrets of RF Design Prof. Tom Lee Stanford University Director, DARPA Microsystems Technology Office Inaugural IEEE SSCS Webinar

Tom Lee, 6/26/2012

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Why y RF design g is hard • Can’t ignore parasitics. • Can’t squander device power gain. • Can’t tolerate much noise or nonlinearity. • Can’t expect accurate models, but you still have to ship anyway.

Tom Lee, 6/26/2012

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Traditional RF design g flow • • • •

Don pointy wizard hat. Obtain chicken. dragoart.com Design first-pass circuit. Mumble obscure Latin incantations (“semper ubi sub ubi...omnia pizza in octo partes di divisa isa est est...e e pl pluribus rib s nihil”) nihil”). • Test circuit; weep uncontrollably. • Adjust Adj t chicken. hi k

Tom Lee, 6/26/2012

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Dark secrets: A p partial list • MOSFETs: What your textbook didn didn’tt tell you • The two-port noise model: Why care? • Optimum noise figure vs. maximum gain

• • • •

To match or not to match – that is the question Linearity and time-invariance time invariance revisited Mixers: Myths and noise Strange impedance behaviors (SIBs)

Tom Lee, 6/26/2012

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MOSFETs: What Your Textbooks May Not Have Told You

Tom Lee, 6/26/2012

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The standard lie

• “Gate-source impedance is a capacitor.” • Because zero power is thus needed to drive it, any output at all all, at any frequency frequency, implies infinite power gain. (The books usually omit that last part.)

Tom Lee, 6/26/2012

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The true story y • Gate-source impedance is not a pure capacitor. • Phase shift associated with finite carrier transit speed d means gate t fi field ld d does nonzero work k on channel charge. • Therefore, power gain is not infinite. • There is also noise associated with the dissipation. Tom Lee, 6/26/2012

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Noisy y channel charge g • Fluctuations couple capacitively to both top and bottom gates. • Induces noisy gate currents. t BottomB tt gate term is ignored by most models and textbooks.

Tom Lee, 6/26/2012

[Shaeffer]

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Sources of noise in MOSFETs • (Thermally-agitated) (Thermally agitated) channel charge charge. • Produces both drain and gate current noise.

• Interconnect resistance. • Series gate resistance Rg is very important important.

• Substrate resistance. • Substrate thermal noise modulates back gate, augments drain current noise in some frequency range. Tom Lee, 6/26/2012

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((All)) FETs and g gate noise: Basic model From channel thermal noise

From gate interconnect Noise already accounted for – Don’t double count!

From induced gate noise

id2  4kTg d 0

Important: p Common error is to define Vgs as across Cgs alone. Tom Lee, 6/26/2012

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Substrate thermal noise Simple model (neglects substrate contribution)

[Goo]

Tom Lee, 6/26/2012

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Substrate thermal noise controversy y • Measuring drain noise at different frequencies has led to confusion about the value of . • Measurements made below ~1GHz 1GHz (i.e., (i e in Region II) may reveal “excess” noise, and a sensitivity to the number of substrate taps, if wrong model is used.

• Early speculations that deep-submicron MOSFET suffer MOSFETs ff from f significant i ifi t enhancement h t off  not borne out. Tom Lee, 6/26/2012

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Gate noise is real;; Murphy p y says y so • Let W  0 while maintaining g resonance and current density (for fixed fT). –G Gain i stays t fixed. fi d – Ibias  0.

• If you ignore gate noise:

W D i noise Drain i Gate noise

– Output noise  zero; absurd to consume zero power and provide noiseless gain. Tom Lee, 6/26/2012

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The Two-Port Noise Model: Why Care?

Tom Lee, 6/26/2012

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Two-port p noise model 2

2

2

= • The IRE chose not to define F directly in terms of equivalent i l t iinputt noise i sources. IInstead: t d Tom Lee, 6/26/2012

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Two-port p noise model Let

and

Tom Lee, 6/26/2012

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Conditions for minimum noise figure g

Tom Lee, 6/26/2012

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Important p observation • Minimum NF and maximum power gain occur for the same source Z only if three miracles occur together: • Gc = 0 ((noise current has no component p in p phase with noise voltage); and • Gu = Gn (conductance ( d t representing ti uncorrelated l t d current noise equals the fictitious conductance that produces noise voltage); p g ); and • Bc = Bin. (correlation susceptance happens to be the same as the actual input susceptance) Tom Lee, 6/26/2012

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To Match or Not to Match -That is the Question

Tom Lee, 6/26/2012

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Impedance p matching: g Why? y • Conjugate match maximizes power transfer. • Terminating a T-line in its characteristic impedance makes the input impedance length-independent. • Also minimizes peak voltage and current along line.

• Selecting and maintaining a standard impedance value (e (e.g., g 50) facilitates fixturing and instrumentation. Tom Lee, 6/26/2012

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Impedance p matching: g Why y not? • Amplifiers generally exhibit best noise figure with a mismatch. i h • M Many amplifiers lifi are more stable t bl or robust b t (i (in th the PVT sense) when mismatched. • If power gain is not in short supply (and stability and noise are not a problem) problem), may not need to match impedances, resulting in a simpler circuit. Tom Lee, 6/26/2012

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Linearity and Time-Invariance: So What?

Tom Lee, 6/26/2012

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LTI,, LTV and all that • A system is linear if superposition holds. • A system is TI if an input timing shift only shifts the timing of the output the same amount. • Shapes p stay y constant.

• If a system is LTI, it can only scale and phaseshift Fourier components. • Output and input frequencies are the same.

• If a system is LTV, input and output frequencies can be different, despite being linear. • If a system is nonlinear, input and output frequencies will generally differ. Tom Lee, 6/26/2012

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Mixers are supposed pp to be linear! • But they are time-varying blocks. • Ignore textbooks and papers that say “mixers mixers are nonlinear…” Mixers are nonlinear in the same way amplifiers are nonlinear: Undesirably.

• Significantly noisier than LNAs for reasons that will be explained shortly. NF values of 10-15dB are not unusual. • Main function of an LNA is usually to provide enough h gain i tto overcome mixer i noise. i Tom Lee, 6/26/2012

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First: This is not a Gilbert mixer • This is a Jones mixer. • Most textbooks and papers (still) wrongly call this a Gilbert cell.

• A true Gilbert cell is a current-domain circuit, and uses predistortion for li linearity. it Tom Lee, 6/26/2012

[Howard Jones] US Pat. Pat #3 #3,241,078 241 078 25

The mixer: An LTV element • Whether Gilbert, Jones or Smith, modern mixers depend on commutation of currents or voltages voltages. • We idealize mixing as the equivalent of multiplying the RF signal by a square-wave LO. • Single Single-balanced balanced mixer: RF signal is unipolar. • Double-balanced mixer: RF signal is DC-free.

• Mixing is ideally linear: Doubling the input (RF) voltage should double the output (IF) voltage. Tom Lee, 6/26/2012

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A multiplier p is an ideal mixer • Key relationship is:

A A cos 1t cos 2t  [cos(1  2 )t  cos(1  2 )t ] 2 • Can be thought of as an amplifier with a timevarying y g amplification p factor.

Tom Lee, 6/26/2012

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Mixer noise figure g • Noise figure of mixers is worse than for LNAs for several reasons. • Noise originating from different RF bands can translate to the same IF. • Transconductor is usually optimized more for linearity th ffor noise. than i • Switching core contributes significant noise in practical mixers.

Tom Lee, 6/26/2012

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Mixer noise figure: g DSB v. SSB • Because noise from two different sidebands (d i d RF and (desired d itits iimage, llocated t d 2fIF away)) can convert to the same IF, need to be careful about defining NF NF. • If both sidebands contain signal (and noise) noise), we report DSB NF. If signal is present in only one sideband, we report SSB NF. • If noise gains are constant, DSB NF = SSB NF – 3dB. • Because DSB NF is lower, it gets reported more frequently. Beware. Tom Lee, 6/26/2012

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Sources of noise in mixers Load structure

Differential switching core

RF diff. amp.

Tom Lee, 6/26/2012

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Mixer noise • Load structure is at the output output, so its noise adds to the output directly; it undergoes no frequency translations. • If 1/f noise is a concern, use PMOS transistors or poly resistor loads.

• Transconductor noise appears at same port as i input t RF signal, i l so it ttranslates l t iin ffrequency th the same way as the RF input. Tom Lee, 6/26/2012

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Dark secret: Switching g noise can dominate • Instantaneous switching not possible possible. • Noise from switching core can actually dominate. • Common Common-mode mode capacitance at tail nodes of core reduces effectiveness of large LO amplitudes.

• Periodic switching of core is equivalent to sampling core noise at (twice) the LO rate. • Frequency translations occur due to this self-mixing.

Tom Lee, 6/26/2012

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Noise contribution of switching g core • As switching transistors are driven through the switching instant, they act as a differential pair for a brief window of time ts. • D During i thi this iinterval, t l th the switching it hi ttransistors i t ttransfer f their drain noise to the output. • Changing drain current implies a changing PSD for the noise; it is cyclostationary.

Tom Lee, 6/26/2012

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Noise contribution of switching g core • The noise contributed by the switching core appears as follows:

TLO/2

• Mathematically equivalent to multiplying a stationary t ti noisy i waveform f by b a sampling li pulse l train with fundamental frequency 2fLO. Tom Lee, 6/26/2012

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Noise contribution of switching g core • Noise at 2nfLO +/- fIF will therefore translate to the IF This noise folding helps explain the relatively IF. poor noise figure of mixers.

2fLO 4fLO

Tom Lee, 6/26/2012

6fLO

8fLO

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Terrovitis mixer noise figure g equation q • A simplified analytical approximation for the SSB noise figure of a Jones mixer is important

FSSB

2g m  4 G  GL  2 2 2 c c g m RS



• Here Here, gm is the transconductance transcond ctance of the bottom differential pair; GL is the conductance of the load; RS is the source resistance resistance, and  is the familiar drain noise parameter. • See [[Terrovitis]] for more complete p version. Tom Lee, 6/26/2012

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Terrovitis mixer noise figure g equation q • The parameter G is the time-averaged transconductance of each pair of switching transistors. For a plain-vanilla Jones mixer,

2 I BIAS G VLO • The parameter  is related to the sampling aperture, and has an approximate value

4   1 t s f LO 3 Tom Lee, 6/26/2012

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Terrovitis mixer noise figure g equation q • The parameter c is directly related to the effective aperture, and is given by

2  sin(t s f LO )  c     t s f LO  • This parameter asymptotically approaches 2/ in the limit of infinitely fast switching switching.

Tom Lee, 6/26/2012

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When Good Amplifiers Go Bad:

Strange Impedance Behaviors

Tom Lee, 6/26/2012

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First: Some simple p transistor models • Can use either gate-source voltage or gate current as independent control variable

• Models are fully equivalent as long as we choose

Tom Lee, 6/26/2012

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View from the gate g • Consider input impedance of the following at 