6.976 High Speed Communication Circuits and Systems Lecture 10 Mixers
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6.976 High Speed Communication Circuits and Systems Lecture 10 Mixers Michael Perrott Massachusetts Institute of Technology Copyright © 2003 by Michael H. Perrott Mixer Design for Wireless Systems Zin From Antenna and Bandpass Filter PC board trace Zo Package Interface Design Issues RF in Mixer IF out To Filter LNA Local Oscillator Output - Noise Figure – impacts receiver sensitivity - Linearity (IIP3) – impacts receiver blocking performance - Conversion gain – lowers noise impact of following stages - Power match – want max voltage gain rather than power match for 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 manufacturable in high volume M.H. Perrott MIT OCW Ideal Mixer Behavior Desired channel RF in(f) 0 -fo fo 1 0 IF out Local Oscillator Output = 2cos(2πfot) Undesired component LO out(f) -fo RF in f ∆f 1 Channel Filter fo f -fo Undesired component IF out(f) -∆f 0 ∆f fo f RF spectrum converted to a lower IF center frequency - IF stands for intermediate frequency If IF frequency is nonzero – heterodyne or low IF receiver If IF frequency is zero – homodyne receiver Use a filter at the IF output to remove undesired high frequency components M.H. Perrott MIT OCW The Issue of Aliasing RF in(f) Image Desired Interferer channel 0 -fo fo -∆f ∆f RF in f Local Oscillator Output = 2cos(2πfot) LO out(f) 1 IF out IF out(f) 1 0 -fo fo f -fo -∆f 0 ∆f f fo When the IF frequency is nonzero, there is an image band for a given desired channel band - Frequency content in image band will combine with that of the desired channel at the IF output - The impact of the image interference cannot be removed through filtering at the IF output! M.H. Perrott MIT OCW LO Feedthrough RF in(f) Image Desired Interferer channel 0 -fo fo -∆f ∆f RF in LO feedthrough f Local Oscillator Output = 2cos(2πfot) LO out(f) 1 IF out(f) 1 0 -fo IF out LO feedthrough fo f -fo -∆f 0 ∆f fo f LO feedthrough will occur from the LO port to IF output port due to parasitic capacitance, power supply coupling, etc. - Often significant since LO output much higher than RF signal M.H. Perrott If large, can potentially desensitize the receiver due to the extra dynamic range consumed at the IF output If small, can generally be removed by filter at IF output MIT OCW Reverse LO Feedthrough RF in(f) Reverse LO feedthrough Image Desired Interferer channel 0 -fo fo -∆f ∆f f RF in Reverse LO feedthrough LO feedthrough Local Oscillator Output = 2cos(2πfot) LO out(f) 1 IF out IF out(f) 1 0 -fo LO feedthrough fo f -fo -∆f 0 ∆f fo f Reverse LO feedthrough will occur from the LO port to RF input port due to parasitic capacitance, etc. - If large, and LNA doesn’t provide adequate isolation, M.H. Perrott then LO energy can leak out of antenna and violate emission standards for radio Must insure that isolate to antenna is adequate MIT OCW Self-Mixing of Reverse LO Feedthrough RF in(f) Reverse LO feedthrough Image Desired Interferer channel 0 -fo fo -∆f ∆f f RF in Reverse LO feedthrough LO feedthrough Local Oscillator Output = 2cos(2πfot) LO out(f) 1 IF out IF out(f) 1 0 -fo Self-mixing of reverse LO feedthrough LO feedthrough fo f -fo -∆f 0 ∆f f fo LO component in the RF input can pass back through the mixer and be modulated by the LO signal - DC and 2f component created at IF output - Of no consequence for a heterodyne system, but can o cause problems for homodyne systems (i.e., zero IF) M.H. Perrott MIT OCW Removal of Image Interference – Solution 1 RF in(f) Reverse LO feedthrough Image Desired Interferer channel 0 -fo fo RF in Image Rejection Filter f Local Oscillator Output = 2cos(2πfot) -∆f ∆f LO out(f) 1 IF out IF out(f) 1 -fo 0 Self-mixing of reverse LO feedthrough LO feedthrough fo f -fo -∆f 0 ∆f fo f An image reject filter can be used before the mixer to prevent the image content from aliasing into the desired channel at the IF output Issue – must have a high IF frequency - Filter bandwidth must be large enough to pass all channels Filter Q cannot be arbitrarily large (low IF requires high Q) M.H. Perrott MIT OCW Removal of Image Interference – Solution 2 RF in(f) Reverse LO feedthrough Desired channel 0 -fo fo ∆f=0 LO out(f) 1 -fo RF in f Reverse LO feedthrough IF out LO feedthrough Local Oscillator Output = 2cos(2πfot) IF out(f) 1 0 Self-mixing of reverse LO feedthrough LO feedthrough fo f -fo 0 fo Mix directly down to baseband (i.e., homodyne approach) Issues – many! f - With an IF frequency of zero, there is no image band - DC term of LO feedthrough can corrupt signal if time-varying - DC offsets can swamp out dynamic range at IF output 1/f noise, back radiation through antenna M.H. Perrott MIT OCW Removal of Image Interference – Solution 3 RF in(f) a(t) Image Desired Interferer channel RF in 0 -f1 f1 f 2sin(2πf1t) c(t) e(t) 2cos(2πf2t) 2cos(2πf1t) b(t) Lowpass Lowpass IF out 2sin(2πf2t) d(t) g(t) Rather than filtering out the image, we can cancel it out using an image rejection mixer - Advantages - M.H. Perrott Allows a low IF frequency to be used without requiring a high Q filter Very amenable to integration Disadvantage Level of image rejection is determined by mismatch in gain and phase of the top and bottom paths Practical architectures limited to 40-50 dB image rejection MIT OCW Image Reject Mixer Principles – Step 1 RF in(f) a(t) Image Desired Interferer channel RF in 0 -f1 f1 f Lowpass Lowpass Note: we are assuming RF in(f) is purely real right now 1 -f1 Lowpass f1 f -f1 Lowpass f1 M.H. Perrott A(f) 0 f1 f B(f) j j -f1 g(t) 1 1 0 IF out 2sin(2πf2t) d(t) b(t) e(t) 2cos(2πf2t) 2cos(2πf1t) 2sin(2πf1t) c(t) 0 -j f -f1 0 -j f1 f MIT OCW Image Reject Mixer Principles – Step 2 RF in(f) a(t) Image Desired Interferer channel RF in 0 -f1 f1 f Lowpass e(t) 2cos(2πf2t) 2cos(2πf1t) 2sin(2πf1t) c(t) Lowpass 2sin(2πf2t) d(t) b(t) IF out g(t) C(f) 1 -f1 1 1 0 f1 f -f1 0 f1 f D(f) j j f1 -f1 M.H. Perrott 0 -j f -f1 0 -j f1 f MIT OCW Image Reject Mixer Principles – Step 3 C(f) c(t) e(t) 1 D(f) -f2 j 0 f2 2cos(2πf2t) f 2sin(2πf2t) d(t) f 0 -j IF out g(t) E(f) 2 1 -f2 1 1 0 f2 f -f2 0 G(f) 2 f2 0 -j f f f2 1 j -f2 1 1 -f2 f f2 -1 -1 -2 M.H. Perrott MIT OCW Image Reject Mixer Principles – Step 4 E(f) 2 1 G(f) 2 1 0 IF out f f2 f f2 -1 1 -f2 1 -f2 e(t) g(t) -1 -2 IF out(f) Baseband Filter 2 -f2 M.H. Perrott 0 f2 f MIT OCW Image Reject Mixer Principles – Implementation Issues RF in(f) a(t) Image Desired Interferer channel RF in 0 -f1 f1 f Lowpass c(t) 2cos(2πf2t) 2cos(2πf1t) 2sin(2πf1t) e(t) 2sin(2πf2t) Lowpass d(t) b(t) IF out g(t) IF out(f) (after baseband filtering) 2 0 f For all analog architecture, going to zero IF introduces sensitivity to 1/f noise at IF output - Can fix this problem by digitizing c(t) and d(t), and then performing final mixing in the digital domain Can generate accurate quadrature sine wave signals by using a frequency divider M.H. Perrott MIT OCW What if RF in(f) is Purely Imaginary? a(t) Lowpass c(t) e(t) RF in(f) Image Desired Interferer channel j 0 -f1 f1 -j f RF in 2cos(2πf2t) 2cos(2πf1t) 2sin(2πf1t) 2sin(2πf2t) Lowpass d(t) b(t) IF out g(t) IF out(f) (after baseband filtering) 0 f Both desired and image signals disappear! Can we modify the architecture to fix this issue? - Architecture is sensitive to the phase of the RF input M.H. Perrott MIT OCW Modification of Mixer Architecture for Imaginary RF in(f) a(t) Lowpass c(t) e(t) RF in(f) Image Desired Interferer channel j 0 -f1 f1 -j f RF in 2cos(2πf1t) 2sin(2πf1t) 2sin(2πf2t) 2cos(2πf2t) Lowpass d(t) b(t) IF out g(t) IF out(f) (after baseband filtering) 2 0 f Desired channel now appears given two changes Issue – architecture now zeros out desired channel when RF in(f) is purely real - Sine and cosine demodulators are switched in second half of image rejection mixer - The two paths are now added rather than subtracted M.H. Perrott MIT OCW Overall Mixer Architecture – Use I/Q Demodulation 2sin(2πf2t) real part of RF in(f) 1 1 0 -f1 imag. part of RF in(f) j -f1 f1 a(t) f RF in Image Desired Interferer channel 0 f1 f IF out I Lowpass 2cos(2πf1t) 2cos(2πf2t) 2sin(2πf1t) Lowpass 2sin(2πf2t) IF out Q b(t) -j 2cos(2πf2t) IF out(f) (I component) (after baseband filtering) 2 2 0 IF out(f) (Q component) (after baseband filtering) f 0 f Both real and imag. parts of RF input now pass through M.H. Perrott MIT OCW Mixer Single-Sideband (SSB) Noise Figure Noise RF in(f) Image band Desired channel Noise 0 LO out = 2cos(2πfot) IF out(f) LO out(f) 1 -fo 0 fo IF out f fo -∆f ∆f 1 Channel Filter RF in SRF No -fo Image Rejection Filter f -∆f 0 Noise from Desired and Image bands add SRF 2No ∆f f Issue – broadband noise from mixer or front end filter will be located in both image and desired bands - Noise from both image and desired bands will combine - M.H. Perrott in desired channel at IF output Channel filter cannot remove this Mixers are inherently noisy! MIT OCW Mixer Double-Sideband (DSB) Noise Figure Noise RF in(f) Desired channel Noise 0 Channel Filter f fo LO out = 2cos(2πfot) IF out(f) 1 0 Noise from positive and negative frequency bands add 2SRF LO out(f) -fo fo IF out RF in SRF No -fo Image Rejection Filter f 2No -∆f 0 ∆f f For zero IF, there is no image band - Noise from positive and negative frequencies combine, but the signals do as well DSB noise figure is 3 dB lower than SSB noise figure For either case, Noise Figure computed through simulation - DSB noise figure often quoted since it sounds better M.H. Perrott MIT OCW A Practical Issue – Square Wave LO Oscillator Signals RF in Local Oscillator Output = 2sgn(cos(2πfot)) LO out(t) 1 T IF out W T 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 briefly review Fourier transforms (series) to understand this issue M.H. Perrott MIT OCW Two Important Transform Pairs Transform of a rectangle pulse in time is a sinc function in frequency x(t) X(f) T 1 T 2 T 2 t f 1 T Transform of an impulse train in time is an impulse train in frequency T M.H. Perrott s(t) S(f) 1 1 T T t 1 T 1 T f MIT OCW Decomposition of Square Wave to Simplify Analysis Consider now a square wave with duty cycle W/T y(t) W 1 T T t Decomposition in time x(t) s(t) * W 1 t M.H. Perrott 1 T T t MIT OCW Associated Frequency Transforms Consider now a square wave with duty cycle W/T y(t) W 1 T T t Decomposition in frequency W X(f) S(f) 1 W M.H. Perrott 1 T f 1 T 1 T f MIT OCW Overall Frequency Transform of a Square Wave Resulting transform relationship y(t) 1 T W T Y(f) W T t 1 W 1 T f Fundamental at frequency 1/T If W = T/2 (i.e., 50% duty cycle) If amplitude varies between 1 and -1 (rather than 1 and 0) - Higher harmonics have lower magnitude - No even harmonics! - No DC component M.H. Perrott MIT OCW Analysis of Using Square-Wave for LO Signal RF in(f) -fo 0 LO out(f) -3fo -2fo -fo 0 RF in IF out f fo Even order harmonic due to not having an exact 50% duty cycle fo 2fo 3fo f Local Oscillator Output = 2sgn(cos(2πfot)) IF out(f) -3fo 2fo -fo DC component of LO waveform 0 f fo 2fo 3fo Desired Output Each frequency component of LO signal will now mix with the RF input - If RF input spectrum sufficiently narrowband with respect to fo, then no aliasing will occur Desired output (mixed by the fundamental component) can be extracted using a filter at the IF output M.H. Perrott MIT OCW Voltage Conversion Gain RF in(f) A 2 0 -fo f fo ∆f LO out(f) -fo 0 RF in = Acos(2π(fo+∆f)t) IF out LO ouput = Bcos(2πfot) IF out(f) B 2 fo f -fo -∆f 0 ∆f AB 4 fo f Defined as voltage ratio of desired IF value to RF input Example: for an ideal mixer with RF input = Asin(2π(fo + ∆ f)t) and sine wave LO signal = Bcos(2πfot) For practical mixers, value depends on mixer topology and LO signal (i.e., sine or square wave) M.H. Perrott MIT OCW Impact of High Voltage Conversion Gain RF in(f) A 2 0 -fo f fo RF in = Acos(2π(fo+∆f)t) ∆f LO out(f) 0 -fo IF out LO ouput = Bcos(2πfot) IF out(f) B 2 fo f Benefit of high voltage gain Issues with high voltage gain -fo -∆f 0 ∆f AB 4 f fo - The noise of later stages will have less of an impact - May be accompanied by higher noise figure than could be achieved with lower voltage gain - May be accompanied by nonlinearities that limit interference rejection (i.e., passive mixers can generally be made more linear than active ones) M.H. Perrott MIT OCW Impact of Nonlinearity in Mixers Memoryless Nonlinearity A Desired RF in(w) Interferers Narrowband Signal 0 w1 w2 RF in Ideal Mixer Memoryless Nonlinearity C y IF out W Memoryless Nonlinearity B LO signal Ignoring dynamic effects, 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 of the LO signal M.H. Perrott Causes additional mixing that must be analyzed Changes conversion gain somewhat Nonlinearity C will cause self mixing of IF output MIT OCW Primary Focus is Typically Nonlinearity in RF Input Path Memoryless Nonlinearity A Desired RF in(w) Interferers Narrowband Signal 0 Y(w) w 1 w2 Ideal Mixer y RF in W Memoryless Nonlinearity C z IF out x Corruption of desired signal Memoryless Nonlinearity B W w1 w2 2w1 2w2 3w1 3w2 0 w2-w1 2w1-w2 2w2-w1 w1+w2 2w1+w2 2w2+w1 LO signal Nonlinearity B not detrimental in most cases Nonlinearity C can be avoided by using a linear load (such as a resistor) Nonlinearity A can hamper rejection of interferers - LO signal often a square wave anyway - Characterize with IIP3 as with LNA designs - Use two-tone test to measure (similar to LNA) M.H. Perrott MIT OCW The Issue of Balance in Mixers RF in(f) DC component IF out RF in 0 -fo f fo LO sig ∆f LO sig(f) 0 -fo LO IF out(f) feedthrough DC component fo f -fo -∆f 0 ∆f RF feedthrough fo f A balanced signal is defined to have a zero DC component Mixers have two signals of concern with respect to this issue – LO and RF signals - Unbalanced RF input causes LO feedthrough - Unbalanced LO signal causes RF feedthrough Issue – transistors require a DC offset M.H. Perrott MIT OCW Achieving a Balanced LO Signal with DC Biasing Combine two mixer paths with LO signal 180 degrees out of phase between the paths LO sig 1 RF in IF out RF in IF out 0 1 0 LO sig 1 LO sig 0 -1 - DC component is cancelled M.H. Perrott MIT OCW Single-Balanced Mixer I1 VLO VRF(t) DC M1 I2 M2 VLO Io VRF Transconductor Io = GmVRF Works by converting RF input voltage to a current, then switching current between each side of differential pair Achieves LO balance using technique on previous slide - Subtraction between paths is inherent to differential output LO swing should be no larger than needed to fully turn on and off differential pair - Square wave is best to minimize noise from M 1 and M2 Transconductor designed for high linearity M.H. Perrott MIT OCW Transconductor Implementation 1 Io Rs VRF Cbig M1 Rbig Vbias Apply RF signal to input of common source amp - Transistor assumed to be in saturation - Transconductance value is the same as that of the transistor High Vbias places device in velocity saturation - Allows high linearity to be achieved M.H. Perrott MIT OCW Transconductor Implementation 2 Io Rs Cbig M1 Vbias VRF Ibias Apply RF signal to a common gate amplifier Transconductance value set by inverse of series combination of Rs and 1/gm of transistor - Amplifier is effectively degenerated to achieve higher linearity Ibias can be set for large current density through device to achieve higher linearity (velocity saturation) M.H. Perrott MIT OCW Transconductor Implementation 3 Io Rs VRF Cbig M1 Rbig Ldeg Vbias Add degeneration to common source amplifier - Inductor better than resistor - M.H. Perrott No DC voltage drop Increased impedance at high frequencies helps filter out undesired high frequency components Don’t generally resonate inductor with Cgs Power match usually not required for IC implementation due to proximity of LNA and mixer MIT OCW LO Feedthrough in Single-Balanced Mixers Higher order harmonics Higher order harmonics VLO(f)-VLO(f) 0 -fo fo Higher order harmonics -fo-f1 VLO f DC 0 I2 M2 VLO Io VRF Transconductor Io = GmVin f f1 Higher order harmonics I1(f)-I2(f) -fo -fo+f1 0 fo-f1 M1 VRF(t) VRF(f) -f1 I1 fo fo+f1 f DC component of RF input causes very large LO feedthrough - Can be removed by filtering, but can also be removed by achieving a zero DC value for RF input M.H. Perrott MIT OCW Double-Balanced Mixer Higher order harmonics Higher order harmonics VLO(f)-VLO(f) 0 -fo fo I1 VLO f VRF(t) VRF Higher order harmonics -fo-f1 0 f f1 VLO Transconductor Io = GmVin DC Higher order harmonics I1(f)-I2(f) -fo -fo+f1 0 fo-f1 M2 Io VRF(f) -f1 M1 I2 fo fo+f1 f DC values of LO and RF signals are zero (balanced) LO feedthrough dramatically reduced! But, practical transconductor needs bias current M.H. Perrott MIT OCW Achieving a Balanced RF Signal with Biasing Use the same trick as with LO balancing LO sig LO sig 1 VRF(t) RF in IF out 0 VRF(t) 1 DC 1 0 RF in IF out 0 1 signal 0 DC LO sig LO sig IF out LO sig DC component cancels signal component adds 1 VRF(t) DC RF in 0 1 signal 0 LO sig M.H. Perrott MIT OCW Double-Balanced Mixer Implementation I3 VLO VRF(t) M2 Io DC VRF M1 I4 Transconductor Io = GmVRF I1 VLO VLO VRF(t) DC M1 I2 M2 VLO Io VRF Transconductor Io = GmVRF Applies technique from previous slide - Subtraction at the output achieved by cross-coupling the output current of each stage M.H. Perrott MIT OCW Gilbert Mixer I1 I2 LO DC VLO LO DC RF DC RF DC M3 M4 M5 M6 VLO VLO VRF(t) M1 M2 VRF(t) Ibias Use a differential pair to achieve the transconductor implementation This is the preferred mixer implementation for most radio systems! M.H. Perrott MIT OCW A Highly Linear CMOS Mixer Cf1 VLO M1 M2 Cb2 VLO M3 M4 VRF Cb1 VRF Rf1 VIF VIF Rf2 Cf2 Transistors are alternated between the off and triode regions by the LO signal - RF signal varies resistance of channel when in triode - Large bias required on RF inputs to achieve triode operation High linearity achieved, but very poor noise figure M.H. Perrott MIT OCW Passive Mixers RS/2 Cbig VLO 2Ain VRF VIF VLO CL RL/2 RL/2 VLO RS/2 VIF VLO Cbig We can avoid the transconductor and simply use switches to perform the mixing operation - No bias current required allows low power operation to be achieved You can learn more about it in Homework 4! M.H. Perrott MIT OCW Square-Law Mixer LL VRF RL CL VIF VLO M1 Vbias Achieves mixing through nonlinearity of MOS device - Ideally square law, which leads to a multiplication term - Undesired components must be filtered out Need a long channel device to get square law behavior Issue – no isolation between LO and RF ports M.H. Perrott MIT OCW Alternative Implementation of Square Law Mixer LL RL CL VIF Cbig VRF Rbig Vbias M1 Cbig2 Ibias VLO Drives LO and RF inputs on separate parts of the transistor - Allows some isolation between LO and RF signals Issue - poorer performance compared to multiplicationbased mixers - Lots of undesired spectral components Poorer isolation between LO and RF ports M.H. Perrott MIT OCW
