High Speed Communication Circuits and Systems Lecture Mixers Michael H. Perrott March 5, 24 Copyright 24 by Michael H. Perrott All rights reserved.
Mixer Design or Wireless Systems From Antenna and Bandpass Filter Z in PC board Mixer trace Z Package o LNA o 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 2
Ideal Mixer Behavior () Desired channel Channel Filter - o o Δ Local Oscillator Output = 2cos(2π o t) LO out() Undesired component () Undesired component - o o - o -Δ Δ 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 put to remove undesired high requency components 3
he Issue o Aliasing () Image Intererer Desired channel - o o -Δ Δ LO out() Local Oscillator Output = 2cos(2π o t) () - o o - o -Δ Δ 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 put - he impact o the image intererence cannot be removed through iltering at the put! 4
LO Feedthrough () Image Intererer Desired channel - o o -Δ Δ Local Oscillator Output = 2cos(2π o t) LO eedthrough LO out() - o o () LO eedthrough - o -Δ Δ o LO eedthrough will occur rom the LO port to put 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 put I small, can generally be removed by ilter at put 5
Reverse LO Feedthrough () Reverse LO eedthrough Image Intererer Desired channel - o o -Δ Δ Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) LO eedthrough LO out() - o o () LO eedthrough - o -Δ Δ o Reverse LO eedthrough will occur rom the LO port to put 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 6
Sel-Mixing o Reverse LO Feedthrough () Reverse LO eedthrough Image Intererer Desired channel - o o -Δ Δ Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) LO eedthrough Sel-mixing o reverse LO eedthrough LO out() - o o () LO eedthrough - o -Δ Δ o LO component in the put can pass back through the mixer and be modulated by the LO signal - DC and 2 o component created at put - O no consequence or a heterodyne system, but can cause problems or homodyne systems (i.e., zero IF) 7
Removal o Image Intererence Solution () Reverse LO eedthrough Image Intererer Desired channel Image Rejection Filter - o o -Δ Δ Local Oscillator Output = 2cos(2π o t) Sel-mixing o reverse LO eedthrough LO out() - o o () LO eedthrough - o -Δ Δ o An image reject ilter can be used beore the mixer to prevent the image content rom aliasing into the desired channel at the put 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) 8
Removal o Image Intererence Solution 2 () Reverse LO eedthrough Desired channel - o o Δ= LO out() - o o Reverse LO eedthrough Local Oscillator Output = 2cos(2π o t) () LO eedthrough Sel-mixing o reverse LO eedthrough LO eedthrough - o 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 put - / noise, back radiation through antenna 9
Removal o Image Intererence Solution 3 () Image Intererer Desired channel a(t) Lowpass c(t) e(t) 2cos(2π t) 2cos(2π 2 t) - 2sin(2π t) Lowpass 2sin(2π 2 t) b(t) d(t) g(t) Rather than iltering out the image, we can cancel it out using an image rejection mixer - Advantages Allows a low IF requency to be used without requiring a high Q ilter Very amenable to integration - Disadvantage Level o image rejection is determined by mismatch in gain and phase o the top and bottom paths Practical architectures limited to 4-5 db image rejection
Image Reject Mixer Principles Step () Image Intererer Desired channel a(t) 2cos(2π t) Lowpass c(t) 2cos(2π 2 t) e(t) - 2sin(2π t) Lowpass 2sin(2π 2 t) Note: we are assuming () is purely real right now b(t) Lowpass A() d(t) g(t) j - - B() Lowpass j - -j - -j
Image Reject Mixer Principles Step 2 () Image Intererer Desired channel a(t) 2cos(2π t) Lowpass c(t) 2cos(2π 2 t) e(t) - 2sin(2π t) Lowpass 2sin(2π 2 t) b(t) d(t) g(t) C() - - D() j j - -j - -j 2
Image Reject Mixer Principles Step 3 C() c(t) e(t) D() j - 2 2 2cos(2π 2 t) 2sin(2π 2 t) d(t) g(t) -j E() 2 j - 2 2-2 G() 2 2 2-2 -j - - 2 2-2 - 3
Image Reject Mixer Principles Step 4 G() 2 2 E() - 2 2 e(t) g(t) - - 2 2-2 - () Baseband Filter 2-2 2 4
Image Reject Mixer Principles Implementation Issues () Image Intererer Desired channel a(t) Lowpass c(t) e(t) 2cos(2π t) 2cos(2π 2 t) - 2sin(2π t) Lowpass 2sin(2π 2 t) b(t) d(t) g(t) () (ater baseband iltering) 2 For all analog architecture, going to zero IF introduces sensitivity to / noise at put - Can ix this problem by digitizing c(t) and d(t), and then perorming inal mixing in the digital domain Can generate accurate quadrature sine wave signals by using a requency divider 5
What i () is Purely Imaginary? a(t) Lowpass c(t) e(t) j () Image Intererer Desired channel 2cos(2π t) 2cos(2π 2 t) - -j 2sin(2π t) b(t) Lowpass d(t) 2sin(2π 2 t) g(t) () (ater baseband iltering) Both desired and image signals disappear! - Architecture is sensitive to the phase o the put Can we modiy the architecture to ix this issue? 6
Modiication o Mixer Architecture or Imaginary () a(t) Lowpass c(t) e(t) j () Image Intererer Desired channel 2cos(2π t) 2sin(2π 2 t) - -j 2sin(2π t) b(t) Lowpass d(t) 2cos(2π 2 t) g(t) () (ater baseband iltering) 2 Desired channel now appears given two changes - Sine and cosine demodulators are switched in second hal o image rejection mixer - he two paths are now added rather than subtracted Issue architecture now zeros out desired channel when () is purely real 7
Overall Mixer Architecture Use I/Q Demodulation real part o () - 2cos(2π t) imag. part o () j Image Intererer Desired channel a(t) 2sin(2π t) Lowpass Lowpass 2sin(2π 2 t) 2cos(2π 2 t) 2sin(2π 2 t) I - -j b(t) 2cos(2π 2 t) Q () (I component) (ater baseband iltering) () (Q component) (ater baseband iltering) 2 2 Both real and imag. parts o put now pass through 8
Mixer Single-Sideband (SSB) Noise Figure Noise () Image band S RF Desired channel Image Rejection Filter Noise Channel Filter N o - o o LO out = 2cos(2π o t) -Δ Δ LO out() - o o -Δ () Δ Noise rom Desired and Image bands add S RF 2N o Issue broadband noise rom mixer or ront end ilter will be located in both image and desired bands - Noise rom both image and desired bands will combine in desired channel at put Channel ilter cannot remove this - Mixers are inherently noisy! 9
Mixer Double-Sideband (DSB) Noise Figure Noise () S RF Desired channel Image Rejection Filter Noise Channel Filter N o - o o LO out = 2cos(2π o t) LO out() - o o -Δ () 2S RF 2N o Δ Noise rom positive and negative requency bands add For zero IF, there is no image band - Noise rom positive and negative requencies combine, but the signals do as well DSB noise igure is 3 db lower than SSB noise igure - DSB noise igure oten quoted since it sounds better For either case, Noise Figure computed through simulation 2
A Practical Issue Square Wave LO Oscillator Signals LO out(t) Local Oscillator Output = 2sgn(cos(2π o t)) W t Square waves are easier to generate than sine waves - How do they impact the mixing operation when used as the LO signal? - We will briely review Fourier transorms (series) to understand this issue 2
wo Important ransorm Pairs ransorm o a rectangle pulse in time is a sinc unction in requency x(t) X() 2 2 ransorm o an impulse train in time is an impulse train in requency t s(t) S() t 22
Decomposition o Square Wave to Simpliy Analysis Consider now a square wave with duty cycle W/ y(t) W t Decomposition in time x(t) s(t) W * t t 23
Associated Frequency ransorms Consider now a square wave with duty cycle W/ y(t) W t Decomposition in requency W X() S() W 24
Overall Frequency ransorm o a Square Wave Resulting transorm relationship y(t) W Y() W t W Fundamental at requency / - Higher harmonics have lower magnitude I W = /2 (i.e., 5% duty cycle) - No even harmonics! I amplitude varies between and - (rather than and ) - No DC component 25
Analysis o Using Square-Wave or LO Signal () - o o LO out() Even order harmonic due to not having an exact 5% duty cycle Local Oscillator Output = 2sgn(cos(2π o t)) () -3 o -2 o - o o 2 o 3 o -3 o 2 o - o o 2 o 3 o DC component o LO waveorm Desired Output Each requency component o LO signal will now mix with the put - I put spectrum suiciently narrowband with respect to o, then no aliasing will occur Desired output (mixed by the undamental component) can be extracted using a ilter at the put 26
Voltage Conversion Gain () - o o LO out() B 2 - o o A 2 Δ = Acos(2π( o +Δ)t) LO ouput = Bcos(2π o t) () - o -Δ Δ o Deined as voltage ratio o desired IF value to put Example: or an ideal mixer with put = Asin(2 ( o + )t) and sine wave LO signal = Bcos(2 o t) AB 4 For practical mixers, value depends on mixer topology and LO signal (i.e., sine or square wave) 27
Impact o High Voltage Conversion Gain () - o o A 2 Δ = Acos(2π( o +Δ)t) LO ouput = Bcos(2π o t) LO out() B 2 - o o () AB 4 - o -Δ Δ o Beneit o high voltage gain - he noise o later stages will have less o an impact Issues with high voltage gain - May be accompanied by higher noise igure than could be achieved with lower voltage gain - May be accompanied by nonlinearities that limit intererence rejection (i.e., passive mixers can generally be made more linear than active ones) 28
Impact o Nonlinearity in Mixers (w) Intererers Desired Narrowband Signal Memoryless Nonlinearity A y Ideal Mixer Memoryless Nonlinearity C W w w 2 Memoryless Nonlinearity B LO signal Ignoring dynamic eects, we can model mixer as nonlinearities around an ideal mixer - Nonlinearity A will have the same impact as LNA nonlinearity (measured with IIP3) - Nonlinearity B will change the spectrum o the LO signal Causes additional mixing that must be analyzed Changes conversion gain somewhat - Nonlinearity C will cause sel mixing o put 29
Primary Focus is ypically Nonlinearity in RF Input Path (w) Intererers Desired Narrowband Signal Memoryless Nonlinearity A y Ideal Mixer z Memoryless Nonlinearity C Y(w) W w w 2 Corruption o desired signal w 2 -w w w 2 2w 2w 2 3w 3w 2 2w -w 2 2w 2 -w w +w 2 2w +w 2 2w 2 +w W x LO signal Memoryless Nonlinearity B Nonlinearity B not detrimental in most cases - LO signal oten a square wave anyway Nonlinearity C can be avoided by using a linear load (such as a resistor) Nonlinearity A can hamper rejection o intererers - Characterize with IIP3 as with LNA designs - Use two-tone test to measure (similar to LNA) 3
he Issue o Balance in Mixers () DC component - o o Δ LO sig() DC component LO sig () LO eedthrough RF eedthrough - o o A balanced signal is deined to have a zero DC component Mixers have two signals o concern with respect to this issue LO and RF signals - Unbalanced put causes LO eedthrough - Unbalanced LO signal causes RF eedthrough Issue transistors require a DC oset - o -Δ Δ o 3
Achieving a Balanced LO Signal with DC Biasing Combine two mixer paths with LO signal 8 degrees out o phase between the paths LO sig LO sig LO sig - - DC component is cancelled 32
Single-Balanced Mixer I I 2 V LO M M 2 V LO DC V RF (t) V RF I o ransconductor I o = G m V RF Works by converting put voltage to a current, then switching current between each side o dierential pair Achieves LO balance using technique on previous slide - Subtraction between paths is inherent to dierential output LO swing should be no larger than needed to ully turn on and o dierential pair - Square wave is best to minimize noise rom M and M 2 ransconductor designed or high linearity 33
ransconductor Implementation I o R s C big M V RF R big V bias Apply RF signal to input o common source amp - ransistor assumed to be in saturation - ransconductance value is the same as that o the transistor High V bias places device in velocity saturation - Allows high linearity to be achieved 34
ransconductor Implementation 2 I o R s C big M V bias V RF I bias Apply RF signal to a common gate ampliier ransconductance value set by inverse o series combination o R s and /g m o transistor - Ampliier is eectively degenerated to achieve higher linearity I bias can be set or large current density through device to achieve higher linearity (velocity saturation) 35
ransconductor Implementation 3 I o R s C big M V RF R big L deg V bias Add degeneration to common source ampliier - Inductor better than resistor No DC voltage drop Increased impedance at high requencies helps ilter out undesired high requency components - Don t generally resonate inductor with C gs Power match usually not required or IC implementation due to proximity o LNA and mixer 36
LO Feedthrough in Single-Balanced Mixers Higher order harmonics V LO ()-V LO () Higher order harmonics I I 2 - o o V RF () - DC V RF (t) V LO V RF M I o M 2 ransconductor I o = G m V in V LO Higher order harmonics I ()-I 2 () Higher order harmonics - o - - o - o + o - o o + DC component o put causes very large LO eedthrough - Can be removed by iltering, but can also be removed by achieving a zero DC value or put 37
Double-Balanced Mixer Higher order harmonics V LO ()-V LO () Higher order harmonics I I 2 - o o V RF () - DC V RF (t) V LO V RF M I o M 2 ransconductor I o = G m V in V LO Higher order harmonics I ()-I 2 () Higher order harmonics - o - - o - o + o - o o + DC values o LO and RF signals are zero (balanced) LO eedthrough dramatically reduced! But, practical transconductor needs bias current 38
Achieving a Balanced RF Signal with Biasing Use the same trick as with LO balancing DC V RF (t) LO sig LO sig DC V RF (t) signal LO sig LO sig V RF (t) signal LO sig DC component cancels signal component adds DC LO sig 39
Double-Balanced Mixer Implementation I 3 I 4 I I 2 V LO M M 2 V LO V LO M M 2 V LO V RF (t) I o V RF (t) I o DC V RF ransconductor I o = G m V RF DC V RF ransconductor I o = G m V RF Applies technique rom previous slide - Subtraction at the output achieved by cross-coupling the output current o each stage 4
Gilbert Mixer I I 2 LO DC V LO M 3 M 4 M 5 M 6 V LO LO DC V LO RF DC V RF (t) M M 2 RF DC V RF (t) I bias Use a dierential pair to achieve the transconductor implementation his is the preerred mixer implementation or most radio systems! 4
A Highly Linear CMOS Mixer C V LO M M 2 C b R V IF C b2 V IF V LO M 3 M 4 R 2 V RF V RF C 2 ransistors are alternated between the o and triode regions by the LO signal - RF signal varies resistance o channel when in triode - Large bias required on puts to achieve triode operation High linearity achieved, but very poor noise igure 42
Passive Mixers R S /2 C big V LO C L V LO 2A in V RF V IF R L /2 R L /2 V IF V LO V LO R S /2 C big We can avoid the transconductor and simply use switches to perorm the mixing operation - No bias current required allows low power operation to be achieved You can learn more about it in Homework 4! 43
Square-Law Mixer L L R L C L V RF V LO V IF M V bias Achieves mixing through nonlinearity o MOS device - Ideally square law, which leads to a multiplication term - Undesired components must be iltered out Need a long channel device to get square law behavior Issue no isolation between LO and RF ports 44
Alternative Implementation o Square Law Mixer L L R L C L C big V IF M C big2 V RF V bias R big I bias V LO Drives LO and puts on separate parts o the transistor - Allows some isolation between LO and RF signals Issue - poorer perormance compared to multiplicationbased mixers - Lots o undesired spectral components - Poorer isolation between LO and RF ports 45