High Speed Communication Circuits and Systems Lecture 15 VCO Examples Mixers

Voltage Controlled Oscillators (VCO s) L 1 L 2 L V out V out V out V bias C var M 1 M 2 C var M 1 C 1 V s V 1 V cont I bias I bias C var V cont Include a tuning element to adjust oscillation requency - Typically use a variable capacitor (varactor) Varactor replaces (part o) ixed capacitance - Note that some ixed capacitance cannot be removed (transistor junctions, interconnect, etc.) Fixed cap lowers requency tuning range

Model or Voltage to Frequency Mapping o VCO T=1/F vco VCO requency versus V cont L 1 L 2 F vco V out V out C var V cont M 1 V s M 2 C var o F out slope=k v V in I bias V in V bias V bias V cont Model VCO in a small signal manner by looking at deviations in requency about the bias point - Assume linear relationship between input voltage and output requency

Model or Voltage to Phase Mapping o VCO Phase is more convenient than requency or analysis - The two are related through an integral relationship Intuition o integral relationship between requency and phase out(t) 1/F vco = α out(t) 1/F vco = α+ε

Frequency Domain Model o VCO Take Laplace Transorm o phase relationship - Note that K v is in units o Hz/V T=1/F vco L 1 V out L 2 V out Frequency Domain VCO Model C var V cont M 1 V s M 2 C var v in 2πK v s Φ out V in I bias V bias

Varactor Implementation Diode Version Consists o a reverse biased diode junction - Variable capacitor ormed by depletion capacitance - Capacitance drops as roughly the square root o the bias voltage Advantage can be ully integrated in CMOS Disadvantages low Q (oten < 20), and low tuning range (± 20%) V+ V+ V- C var P + N + V- Depletion Region N - n-well P - substrate V + -V -

A Recently Popular Approach The MOS Varactor Consists o a MOS transistor (NMOS or PMOS) with drain and source connected together - Abrupt change in capacitance as inversion channel orms Advantage easily integrated in CMOS Disadvantage Q is relatively low in the transition region - Note that large signal is applied to varactor transition region will be swept across each VCO cycle Watch out or gate-to-bulk capacitance!

A Recently Popular Approach The MOS Varactor

A Method To Increase Q o MOS Varactor LSB C W/L 2C 2W/L to VCO 4C 4W/L W/L Overall Capacitance C var 000 001 010 011 100 101 110 111 Coarse Control MSB Coarse Control V control Fine Control Fine Control V control High Q metal caps are switched in to provide coarse tuning Low Q MOS varactor used to obtain ine tuning See Hegazi et. al., A Filtering Technique to Lower LC Oscillator Phase Noise, JSSC, Dec 2001, pp 1921-1930

Supply Pulling and Pushing L 1 L 2 L V out V out V out V bias C var M 1 M 2 C var M 1 C 1 V s V 1 V cont I bias I bias C var V cont Supply voltage has an impact on the VCO requency - Voltage across varactor will vary, thereby causing a shit in its capacitance - Voltage across transistor drain junctions will vary, thereby causing a shit in its depletion capacitance This problem is addressed by building a supply regulator speciically or the VCO

Injection Locking in Oscillators Recall Barkhausen s Criteria x = 0 e H(jw) y Barkhausen Criteria e(t) Closed loop transer unction Asin(w o t) H(jw o ) = 1 Sel-sustaining oscillation at requency ω o i y(t) Asin(w o t)

Injection Locking Mechanism With the input x=0, the selsustaining oscillation occurs at ω o because At requency small deviation ω away rom ω o, the magnitude o G(jω) is still very large So, what i the input x is a nonzero signal at ω o + ω? I the circuit is purely linear, the output y will contain both the oscillation at ω o and the ampliied input at ω o + ω (superposition)

Injection Locking, Cnt d Oscillator Output Adjustment o G m Peak Detector Desired Peak Value In a real oscillator, the transer unction is non-linear to keep the amplitude constant (either by amplitude eedback or saturating G m characteristic) But, let s irst look at what happens i the oscillator transer unction is linear and i a small amplitude signal is injected at the input x

Intuitive Look at Injection Locking, Linear Case Let s conceptually make the oscillator transer unction linear by letting the output reach a desired amplitude (say 1V) and disengaging the amplitude eedback ater sampling and holding the G m adjustment voltage at that level The value o G m is precisely that would make at that point Assuming nothing drits, the output would be a constant amplitude oscillation at ω o Next, let s see what happens i we inject a sinusoidal signal with a small amplitude, say 10mV, at ω o + ω at input x G(jω) is very large at this requency let s say G(jω) =10,000 at ω=ω o + ω The output will be the superposition o 1V sinusoid at ω o and a 100V sinusoid at ω o + ω

Intuitive Look at Injection Locking, Nonlinear Case I the amplitude eedback is re-engaged, it will lower G m to keep the total amplitude at the desired 1V level. This value o G m would adjusted be ar below what s necessary to sustain oscillation at ω o Thus, only the sinusoid at ω o + ω will appear at the output with an amplitude o 1V. The VCO requency is hence locked to the input requency ω o + ω rather than oscillating at the ree running requency o ω o The injection locking phenomenon can be exploited as an alternative to phase-locked loops (See Tom Lee s book, pp563-566, or p439, 1 st, ed.) Otherwise, the injection locking is troublesome

Example o Undesired Injection Locking For homodyne systems, VCO requency can be very close to that o intererers RF in(w) Intererer Desired Narrowband Signal LNA RF in Mixer W 0 w int w o LO signal LO requency V in - Injection locking can happen i inadequate isolation rom mixer RF input to LO port Follow VCO with a buer stage with high reverse isolation to alleviate this problem

Recent VCO Techniques G m -boosted VCO or lower phase noise Recall g m -boosted LNA lowered noise actor: V dd L d C 1 Out M 2 C 2 M 1 T 1 In k L P L s The apparent g m boost is is the result o the gate and source having 180 o out-o-phase waveorms (it increases V gs ). V B Figure by.

Gm-Boosted VCO Similar concept can be employed or VCO s to lower phase noise. Transormer coupling is possible, but takes up area. Can boost g m just by eeding output back to source A V dd B V dd L 1 V B L 2 V+ V- V+ V ctrl V- C 1 M 1 M 2 C 1 C 1 M 1 M 2 C 1 C 2 IB IB C 2 C 2 IB IB C 2 basic concept sel-biased VCO Figure by. See Xiaoyong Li et. al., Low-Power gm-boosted LNA and VCO Circuits in 0.18µm CMOS 2005 ISSCC Digest o Technical Papers pp. 534-353

Wide Tune Range VCO Davide Guermandi, et. al A 0.75 to 2.2GHz Continuously- Tunable Quadrature VCO, Digest o Technical Papers, 2005 ISSCC pp 536-537 SSBM QVCO Q I Div2 Iout Qout Fvco = [2.2 GHz - 3.3 GHz] 2.75 GHz 20% +- C Q I Div2 Fout = [0.74 GHz - 2.2 GHz] 1.47 GHz 50% +- B "1" "0" A => 1/3 Fvco [0.74 GHz - 1.1 GHz] A B => 1/2 Fvco [1.1 GHz - 1.65 GHz] C => 2/3 Fvco [1.49 GHz - 2.2 GHz] Figure by.

Wide Tune Range VCO, Continued VCO, Divider and SSBM Circuits V dd L L L L C C C C Load MP V dd MP R 1 R 1 R 2 R 2 Q Q Vs1 Vs2 D Wrw D Wrw Mc Mc CK Wck Wck CK Vbias B 1 I o I o B 2 Quadrature VCO Balanced Modulator Figure by.

Very High Frequency VCO V DD λ/4 short stub or 114GHz V pp (114GHz) Ping Chen, et. al. A 114GHz VCO in 0.13µm CMOS Technology, 2005 ISSCC Digest o Technical Papers pp. 404-405 - V o (57GHz) L d2 V ctrl L d1 + V o (57GHz) Buer M 2 C var2 Z tank C var1 Z active V G L g2 R g L g1 Buer M 1 L s2 C s2 C s1 L s1 Figure by.

Recent VCO Techniques R. Aparicio and A. Hajimiri, Circular Geometry Oscillators, ISSCC 2004 Digest o Technical Papers, pp378-379 V DD V DD L - + P1 C L V DD P2 L + Oscillator core - L - + Oscillator core V DD V DD Extra inductance and loss + - L Slab inductors oer higher Q than spiral/circular inductors due to less current crowding and less substrate loss In a conventional oscillator topology, the interconnect adds undesired inductance with loss Circular geometry oscillator removes this problem Figure by.

Circular Oscillator Implementation V DD V DD Virtual Ground L - + + L/2 L/2 - + L + + Virtual Ground Point - + L L/2 + V DD L' L' V DD L' - L/2 - + V DD V DD L/2 V DD L' - + V DD L/2 Oscillator core + + - L + - L/2 L/2 Figure by. Shorts the outputs at DC to remove stable DC operating point Shorts outputs at even harmonics to suppress undesired modes

Die Photo and Measured Results 0.9 mm Pick up loop OSC OSC Circular-Geometry Oscillator Single Frequency VCO Cross Technology SiGe 7HP (CMOS transistors only) I mm Channel Length Center Frequency 5.35GHz 0.18µm 5.36GHz OSC OSC Tuning Range ---- 8.3% Output Power 1dBm Buer V dd 1.4V 1.8V I bias 10mA 12mA BIAS Output BIAS Figure by.

Circular Standing Wave Oscillator D. Ham and W. Andress ISSCC 2004 Digest o Technical Papers, pp380-381

Standing Wave Oscillators Energy Injection Relection λ/4 standing wave oscillator (SWO)** Short Relection Relection Relective boundaries Short Short Relection Relection λ/2 SWO [4][5] Short Short Figure by.

Ring Transmission Line Principle E (energy injection) Wave superposition V(φ) ~ e -jβrφ + e jβrφ ~ cos(βrφ) e -jβrφ e jβrφ φ+2π φ r Standing wave ormation Periodic boundary condition V(φ) = V(φ+2π) Standing wave modes l = nλ (n = 1, 2, 3,...) Dierential ring t-line Figure by.

Circular Standing Wave Oscillator (CSWO) T1 CSWO PSD at port T1-T2 L T2 L1 L2 Q Q R2 R1 ω 0 2ω 0 3ω 0 ω Ater even-mode suppression B2 L B1 L: Loud Q: Quiet Even-mode suppression connection ω 0 2ω 0 3ω 0 ω KEY Figure by.

Die Photo and Measurement Set up Agilent E4448A Spectrum Analyzer V dd 50 Ω Bias-Tee RF probing RF probing Q L L Q Open-collector buer S+ G 2.1 mm S- CSWO core Figure by.

Mixers

Mixer Design or Wireless Systems From Antenna and Bandpass Filter Z in PC board Mixer trace RF in IF out Z Package o LNA To Filter Interace Design Issues Local Oscillator Output - Noise Figure impacts receiver sensitivity - Linearity (IIP3) impacts receiver blocking perormance - Conversion gain lowers noise impact o ollowing stages - Power match want max voltage gain rather than power match or integrated designs - Power want low power dissipation - Isolation want to minimize interaction between the RF, IF, and LO ports - Sensitivity to process/temp variations need to make it manuacturable in high volume

Ideal Mixer Behavior RF in() Desired channel RF in IF out Channel Filter - o 0 o Local Oscillator Output = 2cos(2π o t) LO out() 1 1 Undesired component IF out() Undesired component - o 0 o - o - 0 o RF spectrum converted to a lower IF center requency - IF stands or intermediate requency I IF requency is nonzero heterodyne or low IF receiver I IF requency is zero homodyne receiver Use a ilter at the IF output to remove undesired high requency components

The Issue o Image Aliasing RF in() Image Intererer Desired channel RF in IF out - o 0 o - LO out() 1 1 Local Oscillator Output = 2cos(2π o t) IF out() - o 0 o - o - 0 o When the IF requency is nonzero, there is an image band or a given desired channel band - Frequency content in image band will combine with that o the desired channel at the IF output - The impact o the image intererence cannot be removed through iltering at the IF output!

LO Feedthrough RF in() Image Intererer Desired channel RF in IF out - o 0 o - Local Oscillator Output = 2cos(2π o t) LO eedthrough LO out() 1 1 - o 0 o IF out() LO eedthrough - o - 0 o LO eedthrough will occur rom the LO port to IF output port due to parasitic capacitance, power supply coupling, etc. - Oten signiicant since LO output much higher than RF signal I large, can potentially desensitize the receiver due to the extra dynamic range consumed at the IF output I small, can generally be removed by ilter at IF output

Reverse LO Feedthrough RF in() Reverse LO eedthrough Image Intererer Desired channel RF in IF out - o 0 o - Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) LO eedthrough LO out() 1 1 - o 0 o IF out() LO eedthrough - o - 0 o Reverse LO eedthrough will occur rom the LO port to RF input port due to parasitic capacitance, etc. - I large, and LNA doesn t provide adequate isolation, then LO energy can leak out o antenna and violate emission standards or radio - Must insure that isolate to antenna is adequate

Sel-Mixing o Reverse LO Feedthrough RF in() Reverse LO eedthrough Image Intererer Desired channel RF in IF out - o 0 o LO out() 1 1 - o 0 o - Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) LO eedthrough IF out() Sel-mixing o reverse LO eedthrough LO eedthrough - o - 0 o LO component in the RF input can pass back through the mixer and be modulated by the LO signal - DC and 2 o component created at IF output - O no consequence or a heterodyne system, but can cause problems or homodyne systems (i.e., zero IF)

Removal o Image Intererence Solution 1 RF in() Reverse LO eedthrough Image Intererer Desired channel RF in Image Rejection Filter IF out - o 0 o LO out() 1 1 - o 0 o - Local Oscillator Output = 2cos(2π o t) IF out() Sel-mixing o reverse LO eedthrough LO eedthrough - o - 0 o An image reject ilter can be used beore the mixer to prevent the image content rom aliasing into the desired channel at the IF output Issue must have a high IF requency - Filter bandwidth must be large enough to pass all channels - Filter Q cannot be arbitrarily large (low IF requires high Q)

Removal o Image Intererence Solution 2 RF in() Reverse LO eedthrough Desired channel RF in IF out - o 0 o =0 LO out() 1 1 - o 0 o Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) IF out() LO eedthrough Sel-mixing o reverse LO eedthrough LO eedthrough - o 0 o Mix directly down to baseband (i.e., homodyne approach) - With an IF requency o zero, there is no image band Issues many! - DC term o LO eedthrough can corrupt signal i time-varying - DC osets can swamp out dynamic range at IF output - 1/ noise, back radiation through antenna

Removal o Image Intererence Solution 3, Image Reject Mixer RF r(t) Balanced modulator y(t) -90 o phase shiter Local Oscillator + LPF or BPF IF Output Balanced modulator z(t) -90 o phase shiter ^z(t) Image rejected by similar method to SSB generation Image rejection limited by amplitude and phase matching o RF and LO paths. 40 db image suppression is typical RF ilter can reduce the image urther i necessary, otherwise the RF image reject ilter can be omitted.

Frequency Domain View o Image Reject Mixer

Frequency Domain View o Image Reject Mixer, Cnt d It can be shown that image is rejected regardless o the RF input phase