Mixer Design - University of California,...

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Mixer Design

Prof. Ali M. Niknejad and Dr. Osama Shana’a

U.C. BerkeleyCopyright c© 2014 by Ali M. Niknejad

Niknejad Advanced IC’s for Comm

Mixer Design Issues Part 1


Single Balanced Mixer

LO(+)

LO(−)

IF (+)

IF (−)

RF

The above circuit is an example of a single-balanced mixer.The diff-pair Q2-Q3 behave like a differential amplifier to theLO signal. Q1 acts in this case as a current source in theabsence of the RF signal. With this arrangement, any signal,or noise, occupying the IF band at the LO port will getamplified and transferred right to the mixer output causingsignificant degradation to the mixer NF.


LO Buffer Design

IF (+)

IF (−)

RF

LO(+)

LO(−)

RF

LO Filter

IF Filter

To reduce the sensitivity to LO noise, a bandpass filter isplaced at the LO port to filter out any LO noise at the IFband, as shown above. It is important here to note that theeffect of the LO noise can be highly suppressed if the LOsignal is an ideal square wave with zero rise and fall time.This will be shown shortly.


LO Port Noise

IF (+)

IF (−)

RF

LO(+)

LO(−)

v2LO

The LO noise can be modeled as avoltage source in series with thebase of the diff-pair Q2-Q3. If theLO signal is an ideal square wavefrom a zero source impedance witha large voltage swing, the timeover which both devices are on atthe same time is zero.

Therefore the impact of the LO noise is eliminated. However,if the LO signal has a finite rise and fall time, both Q2 andQ3 will be on at the same time, during LO transitions, actinglike an amplifier to the LO noise as well as to their own noise,degrading the overall mixer NF.


Double Balanced Mixer

+LO

−LO

Q1 Q2 Q3 Q4

Q5 Q6+RF

−RF

LE LE

VB,LO

VB,RF


Double Balanced Mixer

Very good port isolation. This proven to be crucial to achievegood IP2 as will be seen later

They provide decent gain

Can easily be integrated on-chip

Moderate LO drive is needed (typically 600mVpp for bipolar)

Adequate NF in the range of ∼ 6− 12dB SSB, depending ongain and IP3.

In the following, we will discuss the performance of thistopology and the some optimization techniques.


Mixer Gain

The mixer voltage gain is the ratio of the output voltagesignal at the IF frequency to the RF input voltage signal. Ifthe LO is at either peak, one pair of the quad transistors iscompletely off, while the other acts like a cascode device. Inthis case, one can think of the mixer as an amplifier with gainof ∼ RL/ZE , where ∼ RL is the differential load resistor andZE is the degeneration impedance of the input diff-pair, whichis really noting but a Gm stage.

Now, let us assume the LO signal is a perfect square wavenormalized to its peak value (which is large enough to turncompletely one quad or the other). The LO signal can then bewritten as:

VLO =2

πcos(ωLOt) +

1

πcos(3ωLOt) +

1

6πcos(5ωLOt) + · · ·


Mixer Gain (cont)

Therefore, the gain RL/ZE will be modulated by the LOsignal, since the IF signal is the product of RF · LO.Therefore, the gain will suffer a loss of 2/π or 3.9 dB

Gainmix =2

π

RL

ZE

This result assumes that for the input Gm diff pair,1/gm � ZL, and that the device fT � f . Of course, the gainequation is simplified, but it gives some insight.


Gilbert Cell Noise

The noise in the Gilbert cell mixer is divided between theinput Gm cell, the quad and the mixer load. We will addressedeach section separately.

Noise in the Gm cell: The noise in the Gm cell follows more orless the NF optimization theory and technique described inthe single-ended CE NF. However, usually the noise of the Gm

cell is a bit compromised by increasing the emitterdegeneration in order to increase the mixer IP3. This isbecause the mixer linearity has more impact on the overall Rxperformance than its NF (to an extent). The NF contributionof the Gm cell to the overall mixer NF is roughly 1.5 ∼2dB.

Noise due to mixer quad: The noise in the quad has two parts.The first part is simply the folding of the image noise comingfrom the Gm cell, as well as the input source. This happenseven if the mixer quad is totally noiseless. The second sourceof mixer quad noise is the one due to the quad noisy devices.


Mixer Quad Noise

rbv2rb

The noise of the quad is at its maximum when each of thequad devices is conducting an equal amount of current. Thisis because when QD3-QD4 devices are ON at the same time,they act as a simple diff-pair amplifying each other’s noise,which is uncorrelated. This noise adds up at the outputseverely degrading the S/N.

Since the quad diff-pairs are not degenerated, the amplifyinggain of this noise is quite large. The time when both quaddiff-pair are partially on is during the LO transition. Thismeans in order to suppress the quad noise, the LO transition(rise and fall time) must be as sharp as possible and close toan ideal square signal as possible.


Mixer Load Noise

The mixer load also contributes to the overall NF. In low orzero IF receivers, the load is a simple resistor, whose noisecontributes to the mixer NF. In some cases the mixer isconfigured as an OTA (operational transconductanceamplifier) with the mixer output being current. This meansthe mixer is designed to have active loads with high outputimpedance. The noise of such active load can be significant ifnot designed properly. Note that the load noise is referredback to input by dividing it over the mixer Gm, so the largerthe input diff-pair Gm is, the less the load noise contributionbecomes.


Gilbert Cell Linearity

The mixer IP3 is usually limited by the input Gm cell. The 3rdorder linearity of the Gm cell depends on the amount ofdegeneration used, the type of degeneration (inductive orresistive) and the bias current. The reader is referred to [1] forexcellent analysis of mixer Gm linearity. Inductivedegeneration is widely used for its low noise and the higherlinearity it provides compared to resistive or capacitivedegeneration. In highly degenerated input Gm cells withrelatively large bias current, the mixer linearity will be limitedby both Gm stage as well as the mixer quad. The 3rd ordernonlinearity of the mixer quad is discussed in detail in [2].


Mixer IP2

IP2: The mixer IP2 is one of the most important spec forlow-IF or direct conversion receivers. In fact, in some systemslike CDMA, mixer IP2 is the limiting spec in making a directconversion CDMA receiver even feasible. The IP2 of theGilbert-cell mixer relies on circuit symmetry as well as LOdrive duty cycle as will be discussed in detail next.

IM2 generated within the Gm stage: Due to finite linearity ofthe Gm cell, its transfer function can be written as:

Iout = GmVin = gm1Vi + gm2V2i + gm3V

3i + ..


Mixer IP2 (cont)

Let us assume the inputs to the mixer are:

Vi = V1 cos(ω1t) + V2 cos(ω2t)whereω1 − ω2 ≤ ωIF

Substituting Vi into the Gm equation, taking only the secondorder distortion into account yields:

Iout = GmVin = gm2V1V2 cos (ω1 − ω2) t + · · ·


Mixer IM2

Note that the IM2 generated in each half circuit of the Gm

stage diff-pair are equal in both magnitude and sign, assumingperfect matching. This is because of the square exponent inthe distortion equation. Therefore, the IM2 signal shows up asa common-mode signal at the output current of the Gm-stage,and so the differential value of the IM2 is zero, if the Gm cellis perfectly symmetrical. This can be seen in the following:

+Vi

2−Vi

2

gm−Vi

2

2

gmVi

2

2

Vi = V1 cos(ω1t) + V2 cos(ω2t)

Any mismatch in the Gm stage half circuit (due to circuitcomponents or layout) results in a finite differential IM2 atthe output. This low frequency IM2 gets upconverted by theLO when it reaches the quad and so won’t appear at the IF.


Gilbert Quad DC Offset

Any DC offset in the quad can be modeled as a DC voltagesource in series with an offset-free quad.

+

This way, the LO signal driving the offset-free quad can bewritten as:

VLO = Voffset + A cos(ωLOt)

With the IM2 signal coming out of the Gm cell being:

VGm−IM2 = gm2V1V2 cos (ω1 − ω2) t

The IF output then is (after lowpass filter):

VIF = VLO × VGm−IM2 = Voffsetgm2V1V2 cos (ω1 − ω2) t


Reducing IM2

Note that the more the LO signal gets closer to an idealsquare wave (with high enough amplitude), the less the quadDC offset impact on the mixer IP2 becomes.

VLO

Voffset

Switching Thresholds

Reducing IM2 mechanisms due to quad offset:

Minimize offsets in the quad by using optimum size.Use low bias resistors at the base to minimize offsets due betamismatch (for bipolar design)Spend a lot of time optimizing the LO buffer to get thesharpest LO edges possible (5 to 10 V/ns is obtainable inmodern technology)Use 50% duty cycle LO generation scheme


Duty Cycle Mismatch

IM2 due LO duty cycle error:VLO

VDC

if LO does not have an exact 50% duty cycle, some IP2degradation can occur. This is because a none 50% dutyresults in an effective DC offset of the LO signal applied tothe quad. This DC offset will not be different from the offsetdue to the quad circuitry itself in providing a path of the IM2generated within the Gm cell to find its way to the mixeroutput.


IM2 Generated By Quad

RF

LO

BB Load Mismatch

IM2 generated within the quad itself: The output current ofthe Gm cell, carrying the two RF tones, passes through thequad, which acts as a current commutating stage. Beinghighly non-linear, the quad itself has a finite second orderdistortion, resulting in generation of a low-frequency IM2 spurout of the two RF tones. Just like the Gm stage case, the IM2spur is a common-mode signal if the quad circuit is perfectlysymmetric. However, this IM2 generated within the quad,although common-mode, can convert to a differential modesignal at the output of the mixer if the mixer load is notperfectly matched.


IM2 Due to RF ⇒ LO Leakage

If the isolation of mixer ports is not sufficient, appreciableamount of RF input power “leaks” to the LO port causing theRF signal to mix with itself.

VRF = cos(ω1t) + cos(ω2t)

VRF→LO = Vleak [cos(ω1t) + cos(ω2t)]

VIF = VRF × VRF→LO = Vleak [cos(ω1t) + cos(ω2t)]2

= Vleak cos(ω1 − ω2)t

RF

LO


IM2 Due to RF ⇒ LO Leakage (cont)

Extreme care in mixer layout is necessary to ensure proper RFto LO isolation. Use all differential mixer topology (all mixerports being differential)

IM2 due baseband to LO leakage:

The mixer down converts the desired signal as well as theclose in jammers, all of which appear at the mixer output IFport. In some systems the jammers can be as high as 60dBabove the desired signal and can swing as high as 1Vpp at themixer output. If portion of this baseband jammer signal at themixer output leaks to the LO port, it will mix with the largeLO signal within the quad itself and then mix with the RFsignal, generating an inband IM2 spur as shown next.


IM2 due to Jammers

VIF = cos(ω1 − ωLO)t + cos(ω2 − ωLO)t

VRF = cos(ω1t) + cos(ω2t)

VIF→LO = Vleak [cos(ω1 − ωLO)t + cos(ω2 − ωLO)t]

VLO × VIF→LO = Vleak [cos(ω1t) + cos(ω2t)]

VLO × VIF→LO × VRF = AVleak [cos(ω1t) + cos(ω2t)]2

= AVleak cos(ω1 − ω2)t


IM2 due to Jammers (cont)

IM2 due LNA:

The jammers pass first through the LNA, which amplifiesthem before they reach the mixer input. Due to finite secondorder nonlinearity of the LNA, a low frequency IM2 appears atthe LNA output as a result of hammers. If the LNA output isDC coupled to the mixer input, this IM2 will get amplified bythe very large low-frequency gain of the mixer Gm cell,especially if the mixer is inductively generated. This IM2 willhave a similar effect in degrading the mixer IP2 to that duemixer Gm itself. Therefore, it is essential to AC couple theLNA output to the mixer input to prevent such IM2mechanism. Doing so will eliminate the LNA IP2 fromaffecting the receiver IP2 (usually it is mixer and basebandfilter limited).


RF Mixer Design Part 2


BiCMOS Mixer

+LO

−LO

+RF

−RF

CMOS Gm cell has a high IP3 for a given current compared tobipolar with small or even no degeneration. The bipolar quadwill ensure low 1/f noise at the output and fast switching forgood IP2 and IP3. Note that the Gm cell 1/f noise getsupconverted by the quad away from the baseband output.


Passive MOS Commutator

+LO

−LO

+LO

M1

M4

M3

M2

+LO

M1

−LO

M2

+LO

M4

−LO

M3

+RF

−RF

+RF −RF+IF

−IF

+IF

−IF

The advantages of the passive MOS commutating mixer:

very good linearityzero current consumptionno 1/f noise (no DC current)small area

The disadvantages

no gain, rather it has loss ranging from 4 6dBlarge required LO drive, almost rail to rail (powerconsumption!)


Passive Current Commutator

+LO

−LO

+IF

−IF+RF −RF

+LO

LNA output RF current is fed into the passive mixer

no DC current in passive mixer results in low 1/f mixer noise

virtual ground of opamp improves overall linearity since mixeroutput (and associated nonlinear parasitic caps) does notswing in such configuration.

mixer device sizing for min loss and acceptable LO drive.

opamp is designed and device sized for best 1/f noise corner


Passive Mixer Filtering Effect

+LO

–LO

VRF

IRF

ZIF /2 IIF

VIF

+

–

ZIF /2

The RF current is modulated to a baseband current given by

vIF (t) =

(2

πiRF (t) cosωLOt

)∗ ZIF (t)

Due to the lack of isolation in a passive mixer, the RF side ofthe switch is affected by the IF voltage. The RF side sees thevoltage drop across the switch and a modulated basebandwaveform (multiplied by +/-1)

vRF (t) = Rsw iRF (t) +4

π2cosωLOt (iRF (t) cosωLOt ∗ ZIF (t))


Passive Filtering (cont)

VRF (s) =Rsw IRF (s) +1

π2(IRF (s)ZIF (s + jωLO) + IRF (s)ZIF (s − jωLO)+

IRF (s − 2jωLO)ZIF (s − jωLO) + IRF (s + 2jωLO)ZIF (s + jωLO))

We see that the baseband filter response is itself frequencytranslated and converted to a high Q bandpass characteristicat the RF port

Thus the baseband filter can attenuate out of band blockersat the RF port itself. This leads to a high IIP3 for these styleof mixers.

Note that the reverse isolation led to this result. In an activemixer, the Gm stage is isolated from the IF load and nofrequency translation of the load takes place.


Op-Amp Noise Amplification

+LO

−LO

+IF

−IF

+LO

Cp

Rp

Cp

The parasitic capacitor at the mixer input (due to mixer itself,LNA out, or layout) results in an effective switched-capacitorresistor due to the mixer switching action. The value of thisresistor is

Rpar =1

4πfLOCpar


Op-Amp Noise Amplification

the noise of the opamp gets gained up to the output by:

vn opamp out =

(1 +

Rf

Rpar

)vn

to minimize this noise, the LNA inductive load must bedesigned to resonate with all parasitic capacitors at the mixerinput to provide high impedance. This is not a luxury one canafford for broadband design.

The op-amp bias current will also affect the linearity when themixer is driven with a strong signal, or a nearby blocker, andsufficient current drive capability is needed.


Sub-Harmonic Mixer Design

fRF

fLO = 0.5fRF

Sub-Harmonic Mixer

The subharmonic mixer is driven by an LO signal that is aninteger fraction, or subharmonic, of the desired LO frequency.For example, if the RF signal is 2GHz, and the desired LO is2GHz for direct conversion, a subharmonic mixer will bedriven by a 1GHz LO signal. The advantages are:

Lower LO re-radiation through the antenna (LO leakage)Lower LO self mixing (lower DC offset at IF)Relaxed requirement on the device switching speed.Lower LO buffer current


25% LO Waveform

The idea is to generate an LO signal that is half the desiredfrequency, yet is rich with a second harmonic, then somehowuse the second harmonic, along with the RF, to get desired IF.A 50% duty cycle LO has no second harmonic. However a25% duty cycle LO has the desired harmonic.

VLO

TLO

TLO/4

The Fourier series expansion of the above square wave is:

VΦ1 =1

π

[√

2 cos(ω0t) + cos(2ω0t) +

√2

3cos(3ω0t)−

√2

5cos(5ω0t) + ...

]

Where ω0 is the subharmonic LO frequency, which in this caseis half the desired LO frequency.


Sub-Harmonic Mixer

+RF

LO1

LO2

IF

The subharmonic mixer topology uses two identical mixersexcited by two phases of the 25% duty cycles. The RF signalis multiplied by these two delayed 25% LO signals and the IFis added in phase at the output, as shown in the above figure.


Sub-Harmonic Mixer Waveforms

The two LO signals, VF 1 and VF 2 , are T/2 delayed relativeto each other.

VLO

TLO

TLO/4

TLO/2


Sub-Harmonic Waveforms

VΦ2 =1

π

[−√

2 cos(ω0t) + cos(2ω0t)−√

2

3cos(3ω0t) +

√2

5cos(5ω0t) + · · ·

]

Looking at the combined IF output of the subharmonic mixerwe can write:

VIF = VRFVΦ1 + VRFVΦ2 = VRF

[2

πcos(2ω0t)

]As seen, the resulting IF output is the product of the RFsignal and an effective LO that has twice the subharmonic LOfrequency, which is in fact the desired LO. The above analysiswas for only one mixer. The question then, how can one buildquadrature subharmonic mixer for both I and Q channels?The answer comes in the way to generate a sin(2ω0t) LOsignal using similar 25% duty cycle signals as follows.


I/Q Sub-Harmonic MixerVLO

TLO

TLO/8

TLO/85

The LO signal LOF 3 is delayed T/8 relative to LOF 1. LOF 4 isdelayed by T/2 relative to LOF 3.The Fourier series expansion of the above square waves is:

VΦ3 =1

π

[√

2 cos(ω0t −π

2) + sin(2ω0t) +

√2

3sin(3ω0t −

π

2) +

√2

5cos(5ω0t −

π

2) + ...

]

VΦ4 =1

π

[−√

2 cos(ω0t −π

2) + sin(2ω0t)−

√2

3sin(3ω0t −

π

2)−√

2

5cos(5ω0t −

π

2) + ...

]


Generation of LO

Looking at the combined IF output of the subharmonic mixerwe can write:

VIF Q = VRFVΦ3 + VRFVΦ4 = VRF

[2

πsin(2ω0t)

]In order to generate all 4 phases of the subharmonic LOsignals, a divide by 4 prescalar needs to be used. This meansthe VCO needs to run at 4X the subharmonic LO, 2X the RFsignal for direct conversion.

RF

LO1

LO2

LO4

LO3

IFI

IFQ

2f04f0

÷4

V CO


Sub-Harmonic Realization

LO(+)

LO(−)

IF (+)

IF (−)

LO(+)

LO(−)

RF(+) RF(−)

The above is a simplified implementation of one subharmonicmixer. Since a subharmonic mixer is two mixers in one drivenby the same RF input but has two different LO phases, asingle common Gm stage is used.


References

K. Fong, R. G. Meyer “High-Frequency Nonlinearity Analysis ofCommon-Emitter and Differential-Pair Transconductance Stages,” IEEE JSSC,vol. 33, No. 4, April 1998, pp. 548-555.

R. G. Meyer, “Intermodulation in High-Frequency Bipolar TransistorIntegrated-Circuit Mixers,” IEEE JSSC, vol. sc-21, No. 4, August 1986, pp.534-537.

D. Manstretta, M Brandolini and F. Svelto, “Second-Order IntermodulationMechanisms in CMOS Downconverters,” IEEE JSSC, vol. 38, No. 3, March2003.

K. Fong, R. G. Meyer, “Monolithic RF Active Mixer Design,” IEEE TCAS-II,vol. 46, No. 3, March 1999, pp. 231-239.

K. Kivekas, A. Parssinen, K. Halonen, “Characterization of IIP2 and DC-Offsetsin Transconductance Mixers,” IEEE TCAS-II, vol. 48, No. 11, November 2001,pp. 1028-1038.

D. Coffing, E. Main, “Effects of Offsets on Bipolar Integrated Circuit MixerEven-Order Distortion Terms,” IEEE Transaction on Microwave Theory andTechniques, vol. 49, No. 1, January 2001, pp. 23-30.

Steven Maas, Microwave Mixers, Artech House Publishers; 2nd edition,1992,ISBN: 0890066051.


References (cont)

A. Parssinen, J. Jussila, J. Ryynnen, L. Sumanen, and K. I. Halonen, “A 2-GHzwide-band direct conversion receiver for WCDMA applications,” IEEE JSSC,vol. 34, pp. 1893-1903, December 1999.

John R. Long, Miles A. Copeland, Peter Schvan, and Robert A. Hadaway, “Alow-voltage silicon bipolar RF front-end for PCN receiver applications,” IEEEInternational Solid-State Circuits Conference, vol. XXXVIII, pp. 140 - 141,February 1995.

J. C. Rudell, J. Ou, T. Byunghak, C. Chien, F. Brianti, J. Weldon, P. Gray, “A1.9-GHz wide-band IF double conversion CMOS receiver for cordless telephoneapplications,” IEEE JSSC, vol. 32, pp. 2071-2088, December 1997.

M. Valla, G. Montagna, R. Castello, “A 72mW CMOS 802.11a DirectConversion Front-End with 3.5dB NF and 200kHz 1/f Noise Corner,” IEEEJSSC, vol. 40, No. 4, April 2005, pp. 970-977.

D. Leenaerts, W. R. White, “1/f noise in passive CMOS mixer for low and zeroIF integrated receivers,” in Proc. 27th Eur. Solid-State Circuits Conf. Austria2001, pp. 103-107.

Jan Crols, Michel S. J. Steyaert, “A 1.5 GHz highly linear CMOSdownconversion mixer”, IEEE Journal of Solid-State Circuits, vol. 30, pp. 736 -742, July 1995


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