tsek03: radio frequency integrated circuits (rfic) lecture ...7.5 varactors 7.6 constant capacitors....
TRANSCRIPT
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TSEK03: Radio Frequency Integrated Circuits (RFIC)Lecture 7: Passive DevicesTed Johansson, EKS, [email protected]
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Overview�2
• Razavi: Chapter 77.1 General considerations7.2 Inductors7.3 Transformers7.4 Transmission lines7.5 Varactors7.6 Constant capacitors
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.1 General considerations�3
• Reduction of off-chip components => Reduction of system cost. Integration is good!
• On-chip inductors:
• With inductive loads (b), we can obtain higher operating frequency and better operation at low supply voltages.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Bond wires = good inductors�4
• High quality• Hard to model• The bond wires and package pins connecting chip to
outside world may experience significant coupling, creating crosstalk between parts of a transceiver.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.2 Inductors�5
• Typically realized as metal spirals.
• Larger inductance than a straight wire.
• Spiral is implemented on top metal layer to minimize parasitic resistance and capacitance.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
�6
• A two dimensional square spiral inductor is fully specified by the following four quantities:• Outer dimension, Dout• Line width, W• Line spacing, S• Number of turns, N
• The inductance primarily depends on the number of turns and the diameter of each turn
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
�7
Magnetic Coupling Factor
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Inductor Structures in RFICs�8
• Various inductor geometries shown below are result of improving the trade-offs in inductor design, specifically those between (a) quality factor and the capacitance, (b) inductance and the dimensions.
• Note: These various inductor geometries provide additional degrees of freedom but also complicate the modeling task.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Inductance calculations�9
• Closed form inductance equations can be found based on (1) Curve fitting methods, (2) Physical properties of inductors.
• This equation is an empirical formula which estimates inductance of 5 nH to 50 nH square spiral inductor within 10% error:
Am – Metal area , Atot – Total Inductor area
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Inductance calculations�10
• Already modeled inductors in a PDK library may exist• Otherwise: EM simulations• Popular tools:
• Momentum (Keysight), integrated with ADS and Cadence Virtuoso. 2.5 D
• HFSS (Ansoft): 3D• Sonnett• (Asitic in the book: old, student work…)
• Output: linear model (n-port s-parameter)
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Example: Momentum�11
• Technology file with layers, via, resistivities, etc., usually supplied by the PDK vendor.
• Or can be created by a user, if enough information is given in the design manual.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Example: Momentum�12
• Cadence integration (example with transformer = double ind)
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Parasitic Capacitance of Integrated Inductors�13
• Planar spiral inductor suffers from parasitic capacitance because the metal lines of the inductor exhibit parallel plate capacitance and adjacent turns bear fringe capacitance.
Bottom-Plate capacitance Interwinding capacitances
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Self-resonance frequency �14
• The frequency at which an inductor resonates with its own capacitances is called the “self-resonance frequency” (fSR).
• The inductor behaves as a capacitor at frequencies above fSR. For this reason, fSR serves as a measure of the maximum frequency at which a given inductor can be used.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.2.5 Loss Mechanisms: Metal Resistance�15
• Metal resistance Rs of spiral inductor of inductance L1 • Q = Quality factor of the inductor (measure of loss in the
inductor)
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
�16Book ”For example, a 5-nH inductor operating at 5 GHz with an RS of 15.7 ︎ has a Q of 10.”
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
�17
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Loss Mechanisms: Skin Effect �18
• Current distribution in a conductor at (a) Low frequency (b) High frequency
Skin depth = Extra resistance =
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Loss Mechanisms: Current crowding �19
• At fcrit , the magnetic field produced by adjacent turn induces eddy current, causing unequal distribution of current across the conductor width, hence altering the effective resistance of the turn.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Loss Mechanisms: Current crowding �20
• As current flows through a smaller width of conductor, this causes a reduction in the effective area between the metal and substrate, hence there is a reduction in the total capacitance.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.2.6 Inductor Modeling�21
• A constant series resistance Rs model inductor loss for limited range of frequencies.
• A constant parallel resistance Rp model inductor loss for narrow range of frequencies.
• Note: The behavior of Q of inductor predicted by above two models has suggested opposite trends of Q with frequency.
Q = L1 ω/RsQ = Rp /L1 ω
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Modeling Loss by Both Series and Parallel Resistors�22
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Broadband Model of Inductor �23
• At low frequencies current is uniformly distributed thorough the conductor and model reduces to R1||R2||.....||Rn
• As frequency increases the current moves away from the center of the conductor, as modeled by rising impedance of inductors in each branch.
Simplemodel Modelwithskineffect
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Compact inductor models�24
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Symmetrical inductor�25
• Differential circuits can employ a single symmetric inductor instead of two asymmetric inductors. Saves area and have high Q, but higher interwinding capacitance (lower fSR).
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Equivalent Lumped Interwinding Capacitance�26
• We unwind the structure as depicted below, assuming that all unit inductances are equal and so are all unit capacitances.
• Resulting equivalent lumped interwinding capacitance of a symmetrical inductor is typically much larger than capacitance of substrate, dominating self resonance frequency.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Inductor magnetic coupling�27
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Inductors with Ground Shield �28
• This structure allows the displacement current to flow through the low resistance path to ground to avoid electrical loss through substrate.
• Eddy currents through a continuous shield drastically reduce inductance and Q, so a “patterned” shield is used.
• This shield reduces the effect of capacitive coupling to substrate.• Eddy currents of magnetic coupling still flows through substrate.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.3 Transformers�29
• Useful function of transformer in RF Design:• Impedance matching.• Feedback and feedforward with positive and negative polarity.• Single ended to differential conversion and vice-verse.• AC coupling between stages.
• Well-designed transformer:• Low series resistance in primary and secondary windings.• High magnetic coupling between primary and secondary
windings.• Low capacitive coupling between primary and secondary
windings.• Low parasitic capacitance to the substrate.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transformer Structures�30
• Transformer derived from a symmetric inductor:• Segments AB and CD are mutually coupled inductors.• Primary and secondary are identical so this is a 1:1
transformer
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transformer Structures: examples - I�31
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transformer Structures: examples - II�32
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transformer Structures: examples - III�33
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Stacked transformers�34
• Higher magnetic coupling.• Unlike planar structures, primary and secondary can be
identical and symmetrical.• Overall area is less than planar structure.• Larger capacitive coupling compared to planar structure.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transformer modeling�35
• Due to high complexity of models, it is very difficult to find the values of each component from measurement or field simulations.
• Typically n-port with s-parameter tables in the simulators.• Sometimes convergence difficulties, especially when f -> 0.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.4 Transmission lines�36
• When the distance of a connection (wire) is comparable to the wavelength.
• f = 1 GHz => l = 30 cm, f = 100 GHz => 3 mm• More PCB-level aspect + cables, unless very high
frequency circuit.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
• Circuit + PCB: Microstrip lines realized in top-most metal layer and ground plane is in lower metal layer. Hence have minimum interaction between signal line and substrate.
• Characteristic impedance Z0:
Transmission lines�37
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Transmission lines�38
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.5 Varactors�39
• Varactor = voltage dependent capacitor• Important properties:
– capacitance range (vs. voltage)– quality factor (parasitic series resistance)
• Two ways to implement on an IC:– pn-junction (reverse-biased) - older technologies– MOSFET transistor - today
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: pn-junction�40
• Reverse-biased pn-junction (diode)• In most IC:s, the substrate is p- and grounded on the
backside.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: pn-junction�41
• Geometry-dependent parasitics, hard to simulate and model.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: pn-junction�42
• Capacitance for a planar reverse pn-junction at voltage VD
Cj0 = cap at zero voltage
V0 = "built-in potential" (about 0.7 V in silicon)m ≈ 0.3 for CMOS
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: MOSFET�43
• The gate-substrate capacitance of an ordinary MOSFET can also be used as a varactor.
• But characteristics of a normal transistor is not ideal for use as a C vs. V-device.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: MOSFET�44
• Instead, place the NMOS-transistor in an nwell. Now it does not work as a transistor anymore, just a capacitor with better characteristics. This is called an "accumulation-mode" MOS varactor.
• For 65 nm CMOS,Cmin and Cmaxare reached at -/+ 0.5 V.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: MOSFET�45
• The Q of MOS varactors is determined by the resistance between the source and drain terminals.
• Q also varies with C: Q = 1/(ωRC)
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Varactors: MOSFET�46
• Overlap capacitance shifts the C/V characteristic up, yielding a ratio of (Cmax + 2WCov)/(Cmin + 2WCov)
• Typical Cmax/Cmin ratios = 2-4
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Example 7.34�47
• A MOS varactor realized in 65-nm technology has an effective length of 50 nm and a Cov of 0.09 fF/μm. If Cox = 17 fF/μm2, determine the largest capacitance range that the varactor can provide.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
7.6 Constant capacitors�48
• Critical parameters of capacitors used in RF IC design:• Capacitance density• Parasitic capacitance• Q of the capacitor
• MOS capacitor• MIM capacitor• Metal plate (MOM) capacitor• Fringe (grid) capacitor
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
MOS capacitor�49
• One long finger having resistance
• Multiple short fingers having resistance
• Since N fingers appear in parallel, Ron,b = Ron,u/N = Ron,a/N2. That is, the decomposition of the device into N parallel fingers reduces the resistance by a factor of N2.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Metal-Insulator-Metal (MIM) Capacitor�50
• Parallel plate capacitor.• Usually 1-2 additional
masks => thinner insulatorto have better Cox/area.
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Metal-Plate (MOM) Capacitor�51
• Parallel plate capacitor.• This structure employs planes in different metal layers
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TSEK03 Integrated Radio Frequency Circuits 2018/Ted Johansson
Fringe Capacitor�52
• Fringe capacitor consists of narrow metal lines with minimum spacing.
• The lateral electric field between adjacent metal lines leads to a high capacitance density.
• No additional masks or processing.
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