Lecture 20: Passive Mixersrfic.eecs.berkeley.edu/~niknejad/ee142_fa05lects/pdf/lect20.pdfSummary of MOS Switching Mixer MOS passive mixer is very linear. The device is either “on”

EECS 142

Lecture 20: Passive Mixers

Prof. Ali M. Niknejad

University of California, Berkeley

Copyright c© 2005 by Ali M. Niknejad

A. M. Niknejad University of California, Berkeley EECS 142 Lecture 20 p. 1/32 – p. 1/32

Voltage Switching MixersLO

LO

+RF

−RF

IF

RIF

Instead of switching currents, we can also switch thevoltage.

In the above circuit, during the +LO cycle, switch S1activates and feeds the RF to the output directly. In the

LO cycle, switch S2 activates and feeds an invertedRF signal to the output.

This circuit requires good switches that turn on hard(low on-resistance) and turn off well (good isolation).


MOS Switching Mixer

LO

LO

+RF

−RF

IF

RIF

A practical implementationuses MOS devices asswitches. The devices arelarge to minimize theiron-resistance with a limitdetermined by isolation(feed-throughcapacitance).

We see that the RF signalis effectively multiplied by±1 with a rate determinedby the LO signal.

A differential RF signal is created using a balun or feddirectly from a balanced LNA.


MOS Device Feedthrough

Cgs Cgd

CjdCjs

Rbs Rbd

RchCjdCjs

Rbs Rbd

Cgso Cgdo

Cgb

Rbg

G

S D

B

G

S D

B

When the device is “on”, it’s in the triode region. Due tothe low on-resistance, the coupling through thesubstrate and LO path is minimal.

When the device is “off”, the RF and LO leak into the IFthrough the overlap and substrate capacitances.


Summary of MOS Switching Mixer

MOS passive mixer is very linear. The device is either“on” or “off” and does not impact the linearity too much.Since there is no transconductance stage, the linearityis very good.

The downside is that the MOS mixer is passive, orlossy. There is no power gain in the device.

Need large LO drive to turn devices on/off

Need to create a differential RF and LO signal. This canbe done using baluns or by using a differential LNA andLO buffer.


MOS “Ring” Mixer+RF

−RF

LO

LO

LO

LO

IF

The RF/LO/IF are all differential signals. During thepositive LO cycle, the RF is coupled to the IF port withpositive phase, whereas during the negative phase theRF is inverted at the IF.

The MOS resistance forms a voltage divider with thesource and load and attenuates the signal as before.


Passive Mixer LO Power

LO

RF IF

LO

RF IF

Since gates of the MOS switches present a largecapacitive load, a buffer is needed to drive them.

The LO buffer can be realized using larger inverters(approach “square wave”) or as a tuned buffer. A tunedlowers the power by roughly Q but has a sinusoidalwaveform .


LO Power (cont)

For an inverter chain driving the LO port, the powerdissipation of the last stage is given by

Pinv = CV 2

LOfLO

C is the total load presented to the LO (two MOSdevices for the double balanced mixer, one MOS devicefor single balanced).

VLO is the LO amplitude to fully turn the devices on andoff. The devices should be biased near threshold. fLO

is the LO frequency.


Tuned LO Power

For the tuned load case, the power is given by

Ptuned =V 2

LO

2Rt

Rt is the effective shunt resistance of the tank. Sincethe tank Q = ωLORtC, we have

Ptuned =V 2

LO

2QωLOC =

πCV 2

LOfLO

Q

A high Q tank helps to reduce the power consumptionof the LO buffer.


H-Bridge Ring Mixer+RF

−RF

IF LOLO

If PMOS devices are available, two CMOS invertersform an H-Bridge, applying the RF input signal to the IFdirectly during the LO cycle and inverting the RF inputat the IF output in the LO cycle.

PMOS and NMOS devices are sized appropriately tomaximize on-conductance and to minimize offcapacitance.

A. M. Niknejad University of California, Berkeley EECS 142 Lecture 20 p. 10/32 – p

RF Driver Stage

+RF

− RF

LO

LO

LO

LO

IF

L1

L2

C3 L3

Rs/2

Rs/2

If the LNA is differential, then the RF port can be driventhrough a LC matching network to maximize the RFvoltage amplitude presented to the mixer.

Note that C3 = C ′

3+ C ′′

3. The capacitance C ′

3and L3 are

used to form a resonant circuit at the RF port. Theinductor L1 and C ′′

3form an L-matching network to

boost the source RF voltage.A. M. Niknejad University of California, Berkeley EECS 142 Lecture 20 p. 11/32 – p

RF Driver Stage (cont)

+RF

L1

L3

Rs/2

C ′

3

C ′′

3

The above figure is the single-ended half circuit. Therole of the tank and L-match are now clearly dilineated.

The voltage gain of the L-match is given by

vRF = vinRt

Rt + (1 + Q2)Rs

√

Q2 + 1

where

Q =ωRF (L1 + L2)

Rs


Time-Varying Conductance

+ IF −

+RF

−RF

g(t)

g(t− TLO/2)g(t)

g(t− TLO/2)

The RF voltage is appliedto a time varying conduc-tance. Note that if theconductance of a the LOswitches is given by g(t),then the conductance ofthe LO switches is given byg(t TLO/2).

The Thevinin equivalent source voltage is given by theopen circuit voltage

vT = vRF

(

g(t)

g(t) + g(t TLO/2)

g(t TLO/2)

g(t) + g(t TLO/2)

)

vT = vRF

(

g(t) g(t TLO/2)

g(t) + g(t TLO/2)

)

= m(t)vRF


Time-Varying Gain m(t)

For the MOS device and a given LO waveform, thefunction m(t) can be calculated and the Fourierexpansion can be used to derive the gain.

In parctice there is a load capacitance CIF at the IF portto filter the downconverted signal. This CL complicatesthe analysis but interested students are encouraged toread the paper by Shahani, Shaeffer and Lee (JSSCvol. 32, Dec 1997, p. 2061-1071)


“Passive” Current Mixer+LO

−LO

+IF

−IF+RF −RF

+LO

The input stage is a Gm stage similar to a Gilbert cellmixer. The Gilbert Quad, though, has no DC currentand switches on/off similar to a passive mixer.

The output signal drives the virtual ground of adifferential op-amp. The current signal is converted intoa voltage output by gthe op-amp.


Advantages of “Passive” Current Mixer

No DC current in quad implies that there is no flickernoise generated by the switching quad. This is the keyadvantage.

The linearity is very good since the output signal is acurrent. The voltage swing does not limit the linearity ofthe mixer. This is to be contrasted to a Gilbert cell mixerwhere the voltage swing is limited due to the headroomof the switching mixer and the transconductance stage.

The op-amp output stage can be converted into an IFfilter (discussed later)


Disadvantages of Mixer

Need large LO drive compared to the active Gilbert cellmixer.

Need an op-amp. This requires extra powerconsumption and introduces additional noise.

Need a common mode feedback circuit at the input ofthe op-amp.


Ring or Quad?+LO

−LO

+LO

M1

M4

M3

M2

+LO

M1

−LO

M2

+LO

M4

−LO

M3

+RF

−RF

+RF −RF+IF

−IF

+IF

−IF

Note that the Gilbert quad is really a folded ring. Thusthe passive and active mixers are very similar. Themain difference is how the quad devices are biased. Inthe Gilbert cell they are biased nominally in saturationand have DC current. In the passive mixers, they arebiased near the threshold.


Op-Amp Noise+LO

−LO

+IF

−IF

+LO

Cp

Rp

Cp

The op-amp input referred noise is amplified to IF. Theresistance seen at the op-amp input terminals isactually a switched capacitor resistor!

The parasitic capacitance at the output of thetransconductance stage is charged and discharged atthe rate of the LO.


Switched Capacitor Resistor+LO

−LO

Cp

Ix

+Vx

−

x

+V−

Note that the parasitic capacitances are charged at therate of the LO to the input voltage Vx, and then to the

Vx, every cycle.

The total charge transferred during a period is given by

Qtot = CpVx ( CpVx) = 2CpVx

The net current is given by Ix = Qtot

TLO= 2CpVxfLO


Switched Capacitor Resistor (cont)

Since there are two differential pairs connected to theop-amp terminals in parallel, the total charge is twice.So the effective resistance seen at this node is given by

Rp =Vx

2Ix

The effective resistance is therefore given by

Rp =1

4fLOCp

This is a switched capacitor “resistors”.


Op-Amp Noise Transfer

+IF

−IF

Rp

Rp

Rf

Rf

The noise is thus transferred to the output with transferfunction given by

v2o =

(

1 +2Rf

Rp

)2

v2amp

To minimize this noise, we have to minimize theparasitic capacitance Cp and the op-amp noise.


Output Filter Stage

RF

LO

IF Filter

+IF

−IF

Since a down-conversion mixer will naturally drive afilter, we see that the output current can be useddirectly to drive a current mode filter.

For instance, the op-amp can be absorbed into the firststage of a multi-stage op-amp RC IF filter. Thefeedback resistor Rf is shunted with a capacitor Cf toproduce a pole.


Diode Mixers

Bias

RF

IF

LO RIFC0

L∞

If MOS devices are not available, or if the frequencyexceeds the capability of the MOS devices, diodes canbe used as switch elements.

Here the diode is biased into “on” state by the chokesand bypass capacitors. A strong LO signal, though, canturn the diode off.


Weak LO Diode Mixer

RF

IF

LO RF IF

RFLO +

The RF signal “riding” on top of the LO signal is thusmixed by the switching action.

Note that if the LO signal is weak, then mixing actionoccurs by the non-linearity of the diode. But this modehas a smaller conversion gain and produces moredistortion.


Diode Ring Mixer

RF

IF

LO

RIF

D1

D4

D3

D2

The ring mixer is a passive mixer. Typical loss numbersare about 6 dB. The mixer has good isolation. TheLO ←→ RF isolation comes from the transformers. Thebalanced operation results in RF and LO rejection.

The LO signal drive is large since it must turn on/offdiodes.


Mixer Description

The ring mixer is a fully balanced mixer but we have theoption of driving the LO and RF single ended. As weshall see, the LO signal alternatively turns on diodesD1/D2 or D3/D4 thereby connecting the RF voltage tothe IF with alternatively polarity.

During a positive LO voltage, the secondary of the LOtransformer applies a positive voltage across D1 inseries with the load R thereby forward biasing the diode.

Likewise, the secondary terminal of the LO transformerapplies a negative voltage to the cathode of D2, therebyforward biasing it in series with the load.

Diodes D3/D4 are reverse biased and therefore opencircuits (ideally).


Positive LO Cycle

RF

IF

LO

RIF

Zi = 0

+

vs

−

+vs

N

−

The equivalent circuit above shows small resistorrepresenting the diode on resistance.

The RF signal is applied to the load through the centertap of the transformer. We shall show that theimpedance looking into the transformer is low (ideallyzero), and thus the entire RF signal at the secondaryterminal is applied to the load vo = vs/N


LO Transformer

+vx

−

Zi =vx

ix

i1

i2

ZLO

Note the input impedance looking into the LOtransformer is ideally short circuit. To see this, apply atest voltage vx to this node.

If we ignore the effect of the LO signal for now, we seethat two equal currents i1 = i2 = ix/2 flow into thesecondary of the LO transformer. The return currentcomes from the center tap ground.


LO Transformer (cont)

The induced voltage at the primary is given by

v1 = jω(M12 M13)ix/2 ≡ 0

This is because M13 = M12 and the currents on thesecondary are out of phase.

The voltages induced on the secondary side arelikewise zero (assuming perfect coupling)

v2 = jωL2ix/2 + jωM23( ix/2) ≡ 0

v3 = jωL3( ix/2) + jωM32ix/2 ≡ 0


Negative LO CycleRF

IFRIF

Zi = 0

+

vs

−

+vs

N

−

LO

By symmetry, during the negative LO cycle, the mixersimplifies to the above equivalent circuit.

During this cycle, the RF signal is applied to the loadthrough the center tap and the bottom of thetransformer, thus producing an output signal in phasewith the RF

vo = +vs/N


Diode Ring Mixer OperationThe operation is thus similar to the double balancedGilbert cell mixer in voltage mode. The RF voltage ismultiplied by ±1 with a rate of the LO signal.

The lack of DC means that the RF is rejected at the IFport. Likewise, the LO/RF signals are isolated by theswitches. The only feed-through occurs due to reverseisolation of the diodes.

The biggest drawback, though, is the bulkytransformers and the large LO drive. The mixer is verylinear and quite attractive in applications where linearityreigns supreme over power consumption.

At microwave frequencies, the transformers can bereplaced by couplers. Since diodes can operate up toextremely high frequencies (THz), the entire circuit canwork up to THz region.


Documents

Lecture 20: Passive Mixersrfic.eecs.berkeley.edu/~niknejad/ee142_fa05lects/pdf/lect20.pdfSummary of MOS Switching Mixer MOS passive mixer is very linear. The device is either “on”