High Speed Communication Circuits and Systems Lecture 10 Mixers

Transcription

1 High Speed Communication Circuits and Systems Lecture Mixers Michael H. Perrott March 5, 24 Copyright 24 by Michael H. Perrott All rights reserved.

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 Image Reject Mixer Principles Step 3 C() c(t) e(t) D() j cos(2π 2 t) 2sin(2π 2 t) d(t) g(t) -j E() 2 j G() j

14 Image Reject Mixer Principles Step 4 G() 2 2 E() e(t) g(t) () Baseband Filter

15 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

16 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

17 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

18 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

19 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

20 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

21 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

22 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

23 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

24 Associated Frequency ransorms Consider now a square wave with duty cycle W/ y(t) W t Decomposition in requency W X() S() W 24

25 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

26 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

27 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

28 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

29 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

30 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

31 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

32 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

33 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

34 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

35 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

36 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

37 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

38 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

39 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

40 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

41 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

42 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

43 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

44 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

45 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