1130 半导体学报 第29卷 the transconductor staget.To compare the transcon- -Q-mixer -G-mixer ductor nonlinearity of the Q-mixer and G-mixer,we first analyze the nonlinearity of the common source short-channel MOSFET,whose I-V relation ists] 1=水深 (10) -1.0 -0.5 0 0.5 Normalized time.TLo where I is the drain current and Vasr=Vas-Vr is the gate overdrive voltage.Parameter K depends on Fig.3 Ideal transfer waveform of switching pair the technology and the size of the device,and is pro- portional to the channel width.Parameter 0 models to through each of the four switching transistors for one a first order the source series resistance,the mobility quarter of the LO period.The corresponding transfer degradation due to the vertical field,and the velocity waveform has the Fourier series expansion saturation due to the lateral field in the short-chan- fo(t)= 1 4 sin(k元/4×(1-ekr)×euo nel.0 depends on the channel length and is independ- kπ/4 ent of the body effect.The third-order input-intercept (5) point of this MOSFET can be derived as The transfer gain of switching pair equals the IIP3 =4Vcsr(2 +avasr)(1+VT) (11) Fourier coefficient of the fundamental LO frequency, 30 which means According to Eq.(11),IIP3 is a monotonically Gsw.6=2/π (6) increasing function of Vosr.The transconductor tran- Gsw.0=√2/π (7) sistors of the Q-mixer and G-mixer have the same Gsw.0 Gsw.G/V2 (8) channel length and gate overdrive voltage,and there- Combining Eqs.(1),(2),(3),and (8),we con- fore exhibit similar linearity. In fact,as the Q-mixer has a larger parasitic ca- clude that pacitance at the drain of a transconductor transistor CGo=√ECGa (9) than the G-mixer,the nonlinearity caused by the Thus,in commutating mode,the Q-mixer has a switching pair is somewhat larger.This is because 3dB improvement in CG over the G-mixer.Figure 4 when the LO amplitude is high,higher current is in- plots the simulated CG of these two topologies versus jected by the parasitic capacitances,which attenuates LO amplitude.In non-commutating mode,the two to- the high-frequency phenomena and alters the periodic pologies have similar CG,but when the LO amplitude operating point of the devicests].However,because is high and the mixers are operating in the commuta- this switching pair is a minor nonlinearity contributor ting mode,the CG of the Q-mixer is approximately in commutating mixers,this linearity loss is negli- 2.8dB greater than the G-mixer.The slight discrepan- gible cy between 2.8 and 3dB is due to the larger parasitic capacitance at the drain of the transconductor tran- 2.3 Noise analysis sistors. Output noise of the mixer derives from the load 2.2 Linearity analysis stage,switching stage,and transconductor stage,in different proportions and from different frequencies. In commutating mixers,the linearity is limited by The loads of the mixer contribute noise in the in- termediate frequency (IF).Since the loads of the Q- 10 mixer and G-mixer are identical,the output noise due 8 to the load stage is also the same,with power spectral 6 density (PSD) 4 Vi.Lod 4kTRL (12) 2 0 -G-mixer As far as the mixer is concerned,noise origina- Q-mixer ting in the transconductor stage is indistinguishable from the RF input signal,so the noise at frequencies 0.2 0.40.6 0.8 1.0 fo±fir,3fio±fr,5fio±fr…is down-converted to LO amplitude/V IF at output,in the same way as the input signalte. Fig.4 Simulated CG of Q-mixer and G-mixer versus LO ampli- Thus,the transconductor stage contributes only white tude noise to the output noise if the switching transistors半 导 体 学 报 第２９卷 犉犻犵．３ 犐犱犲犪犾狋狉犪狀狊犳犲狉狑犪狏犲犳狅狉犿狅犳狊狑犻狋犮犺犻狀犵狆犪犻狉 狋犺狉狅狌犵犺犲犪犮犺狅犳狋犺犲犳狅狌狉狊狑犻狋犮犺犻狀犵狋狉犪狀狊犻狊狋狅狉狊犳狅狉狅狀犲 狇狌犪狉狋犲狉狅犳狋犺犲犔犗狆犲狉犻狅犱．犜犺犲犮狅狉狉犲狊狆狅狀犱犻狀犵狋狉犪狀狊犳犲狉 狑犪狏犲犳狅狉犿犺犪狊狋犺犲犉狅狌狉犻犲狉狊犲狉犻犲狊犲狓狆犪狀狊犻狅狀 犳犙（狋）＝ １ ４ ∑ ∞ 犽＝－∞ 狊犻狀（犽π／４） 犽π／４ × （１－犲－犼犽π）×犲犼犽ω犔犗狋 （５） 犜犺犲狋狉犪狀狊犳犲狉犵犪犻狀狅犳狊狑犻狋犮犺犻狀犵狆犪犻狉犲狇狌犪犾狊狋犺犲 犉狅狌狉犻犲狉犮狅犲犳犳犻犮犻犲狀狋狅犳狋犺犲犳狌狀犱犪犿犲狀狋犪犾犔犗犳狉犲狇狌犲狀犮狔， 狑犺犻犮犺犿犲犪狀狊 犌犛犠，犌 ＝２／π （６） 犌犛犠，犙 ＝ 槡２／π （７） 犌犛犠，犙 ＝ 犌犛犠，犌／槡２ （８） 犆狅犿犫犻狀犻狀犵犈狇狊．（１），（２），（３），犪狀犱 （８），狑犲犮狅狀 犮犾狌犱犲狋犺犪狋 犆犌犙 ＝ 槡２犆犌犌 （９） 犜犺狌狊，犻狀犮狅犿犿狌狋犪狋犻狀犵 犿狅犱犲，狋犺犲 犙犿犻狓犲狉犺犪狊犪 ３犱犅犻犿狆狉狅狏犲犿犲狀狋犻狀犆犌 狅狏犲狉狋犺犲犌犿犻狓犲狉．犉犻犵狌狉犲４ 狆犾狅狋狊狋犺犲狊犻犿狌犾犪狋犲犱犆犌狅犳狋犺犲狊犲狋狑狅狋狅狆狅犾狅犵犻犲狊狏犲狉狊狌狊 犔犗犪犿狆犾犻狋狌犱犲．犐狀狀狅狀犮狅犿犿狌狋犪狋犻狀犵犿狅犱犲，狋犺犲狋狑狅狋狅 狆狅犾狅犵犻犲狊犺犪狏犲狊犻犿犻犾犪狉犆犌，犫狌狋狑犺犲狀狋犺犲犔犗犪犿狆犾犻狋狌犱犲 犻狊犺犻犵犺犪狀犱狋犺犲犿犻狓犲狉狊犪狉犲狅狆犲狉犪狋犻狀犵犻狀狋犺犲犮狅犿犿狌狋犪 狋犻狀犵犿狅犱犲，狋犺犲犆犌 狅犳狋犺犲 犙犿犻狓犲狉犻狊犪狆狆狉狅狓犻犿犪狋犲犾狔 ２８犱犅犵狉犲犪狋犲狉狋犺犪狀狋犺犲犌犿犻狓犲狉．犜犺犲狊犾犻犵犺狋犱犻狊犮狉犲狆犪狀 犮狔犫犲狋狑犲犲狀２８犪狀犱３犱犅犻狊犱狌犲狋狅狋犺犲犾犪狉犵犲狉狆犪狉犪狊犻狋犻犮 犮犪狆犪犮犻狋犪狀犮犲犪狋狋犺犲犱狉犪犻狀狅犳狋犺犲狋狉犪狀狊犮狅狀犱狌犮狋狅狉狋狉犪狀 狊犻狊狋狅狉狊． ２．２ 犔犻狀犲犪狉犻狋狔犪狀犪犾狔狊犻狊 犐狀犮狅犿犿狌狋犪狋犻狀犵犿犻狓犲狉狊，狋犺犲犾犻狀犲犪狉犻狋狔犻狊犾犻犿犻狋犲犱犫狔 犉犻犵．４ 犛犻犿狌犾犪狋犲犱犆犌狅犳犙犿犻狓犲狉犪狀犱犌犿犻狓犲狉狏犲狉狊狌狊犔犗犪犿狆犾犻 狋狌犱犲 狋犺犲狋狉犪狀狊犮狅狀犱狌犮狋狅狉狊狋犪犵犲［４］ ．犜狅犮狅犿狆犪狉犲狋犺犲狋狉犪狀狊犮狅狀 犱狌犮狋狅狉狀狅狀犾犻狀犲犪狉犻狋狔狅犳狋犺犲犙犿犻狓犲狉犪狀犱 犌犿犻狓犲狉，狑犲 犳犻狉狊狋犪狀犪犾狔狕犲狋犺犲狀狅狀犾犻狀犲犪狉犻狋狔狅犳狋犺犲犮狅犿犿狅狀狊狅狌狉犮犲 狊犺狅狉狋犮犺犪狀狀犲犾犕犗犛犉犈犜，狑犺狅狊犲犐犞狉犲犾犪狋犻狅狀犻狊［５］ 犐 ＝ 犓 犞２ 犌犛犜 １＋θ犞犌犛犜 （１０） 狑犺犲狉犲犐犻狊狋犺犲犱狉犪犻狀犮狌狉狉犲狀狋犪狀犱犞犌犛犜 ＝犞犌犛 －犞犜犻狊 狋犺犲犵犪狋犲狅狏犲狉犱狉犻狏犲狏狅犾狋犪犵犲．犘犪狉犪犿犲狋犲狉犓 犱犲狆犲狀犱狊狅狀 狋犺犲狋犲犮犺狀狅犾狅犵狔犪狀犱狋犺犲狊犻狕犲狅犳狋犺犲犱犲狏犻犮犲，犪狀犱犻狊狆狉狅 狆狅狉狋犻狅狀犪犾狋狅狋犺犲犮犺犪狀狀犲犾狑犻犱狋犺．犘犪狉犪犿犲狋犲狉θ犿狅犱犲犾狊狋狅 犪犳犻狉狊狋狅狉犱犲狉狋犺犲狊狅狌狉犮犲狊犲狉犻犲狊狉犲狊犻狊狋犪狀犮犲，狋犺犲犿狅犫犻犾犻狋狔 犱犲犵狉犪犱犪狋犻狅狀犱狌犲狋狅狋犺犲狏犲狉狋犻犮犪犾犳犻犲犾犱，犪狀犱狋犺犲狏犲犾狅犮犻狋狔 狊犪狋狌狉犪狋犻狅狀犱狌犲狋狅狋犺犲犾犪狋犲狉犪犾犳犻犲犾犱犻狀狋犺犲狊犺狅狉狋犮犺犪狀 狀犲犾．θ犱犲狆犲狀犱狊狅狀狋犺犲犮犺犪狀狀犲犾犾犲狀犵狋犺犪狀犱犻狊犻狀犱犲狆犲狀犱 犲狀狋狅犳狋犺犲犫狅犱狔犲犳犳犲犮狋．犜犺犲狋犺犻狉犱狅狉犱犲狉犻狀狆狌狋犻狀狋犲狉犮犲狆狋 狆狅犻狀狋狅犳狋犺犻狊犕犗犛犉犈犜犮犪狀犫犲犱犲狉犻狏犲犱犪狊 犐犐犘３＝４犞犌犛犜（２＋θ犞犌犛犜）（１＋θ犞犌犛犜）２ ３θ （１１） 犃犮犮狅狉犱犻狀犵狋狅犈狇．（１１），犐犐犘３犻狊犪 犿狅狀狅狋狅狀犻犮犪犾犾狔 犻狀犮狉犲犪狊犻狀犵犳狌狀犮狋犻狅狀狅犳犞犌犛犜．犜犺犲狋狉犪狀狊犮狅狀犱狌犮狋狅狉狋狉犪狀 狊犻狊狋狅狉狊狅犳狋犺犲 犙犿犻狓犲狉犪狀犱 犌犿犻狓犲狉犺犪狏犲狋犺犲狊犪犿犲 犮犺犪狀狀犲犾犾犲狀犵狋犺犪狀犱犵犪狋犲狅狏犲狉犱狉犻狏犲狏狅犾狋犪犵犲，犪狀犱狋犺犲狉犲 犳狅狉犲犲狓犺犻犫犻狋狊犻犿犻犾犪狉犾犻狀犲犪狉犻狋狔． 犐狀犳犪犮狋，犪狊狋犺犲犙犿犻狓犲狉犺犪狊犪犾犪狉犵犲狉狆犪狉犪狊犻狋犻犮犮犪 狆犪犮犻狋犪狀犮犲犪狋狋犺犲犱狉犪犻狀狅犳犪狋狉犪狀狊犮狅狀犱狌犮狋狅狉狋狉犪狀狊犻狊狋狅狉 狋犺犪狀狋犺犲 犌犿犻狓犲狉，狋犺犲 狀狅狀犾犻狀犲犪狉犻狋狔 犮犪狌狊犲犱 犫狔 狋犺犲 狊狑犻狋犮犺犻狀犵狆犪犻狉犻狊狊狅犿犲狑犺犪狋犾犪狉犵犲狉．犜犺犻狊犻狊犫犲犮犪狌狊犲 狑犺犲狀狋犺犲犔犗犪犿狆犾犻狋狌犱犲犻狊犺犻犵犺，犺犻犵犺犲狉犮狌狉狉犲狀狋犻狊犻狀 犼犲犮狋犲犱犫狔狋犺犲狆犪狉犪狊犻狋犻犮犮犪狆犪犮犻狋犪狀犮犲狊，狑犺犻犮犺犪狋狋犲狀狌犪狋犲狊 狋犺犲犺犻犵犺犳狉犲狇狌犲狀犮狔狆犺犲狀狅犿犲狀犪犪狀犱犪犾狋犲狉狊狋犺犲狆犲狉犻狅犱犻犮 狅狆犲狉犪狋犻狀犵狆狅犻狀狋狅犳狋犺犲犱犲狏犻犮犲狊［５］ ．犎狅狑犲狏犲狉，犫犲犮犪狌狊犲 狋犺犻狊狊狑犻狋犮犺犻狀犵狆犪犻狉犻狊犪犿犻狀狅狉狀狅狀犾犻狀犲犪狉犻狋狔犮狅狀狋狉犻犫狌狋狅狉 犻狀犮狅犿犿狌狋犪狋犻狀犵 犿犻狓犲狉狊，狋犺犻狊犾犻狀犲犪狉犻狋狔犾狅狊狊犻狊狀犲犵犾犻 犵犻犫犾犲． ２．３ 犖狅犻狊犲犪狀犪犾狔狊犻狊 犗狌狋狆狌狋狀狅犻狊犲狅犳狋犺犲犿犻狓犲狉犱犲狉犻狏犲狊犳狉狅犿狋犺犲犾狅犪犱 狊狋犪犵犲，狊狑犻狋犮犺犻狀犵狊狋犪犵犲，犪狀犱狋狉犪狀狊犮狅狀犱狌犮狋狅狉狊狋犪犵犲，犻狀 犱犻犳犳犲狉犲狀狋狆狉狅狆狅狉狋犻狅狀狊犪狀犱犳狉狅犿犱犻犳犳犲狉犲狀狋犳狉犲狇狌犲狀犮犻犲狊． 犜犺犲犾狅犪犱狊狅犳狋犺犲犿犻狓犲狉犮狅狀狋狉犻犫狌狋犲狀狅犻狊犲犻狀狋犺犲犻狀 狋犲狉犿犲犱犻犪狋犲犳狉犲狇狌犲狀犮狔 （犐犉）．犛犻狀犮犲狋犺犲犾狅犪犱狊狅犳狋犺犲犙 犿犻狓犲狉犪狀犱犌犿犻狓犲狉犪狉犲犻犱犲狀狋犻犮犪犾，狋犺犲狅狌狋狆狌狋狀狅犻狊犲犱狌犲 狋狅狋犺犲犾狅犪犱狊狋犪犵犲犻狊犪犾狊狅狋犺犲狊犪犿犲，狑犻狋犺狆狅狑犲狉狊狆犲犮狋狉犪犾 犱犲狀狊犻狋狔（犘犛犇） 犞２ 狀，犔狅犪犱 ＝４犽犜犚犔 （１２） 犃狊犳犪狉犪狊狋犺犲犿犻狓犲狉犻狊犮狅狀犮犲狉狀犲犱，狀狅犻狊犲狅狉犻犵犻狀犪 狋犻狀犵犻狀狋犺犲狋狉犪狀狊犮狅狀犱狌犮狋狅狉狊狋犪犵犲犻狊犻狀犱犻狊狋犻狀犵狌犻狊犺犪犫犾犲 犳狉狅犿狋犺犲犚犉犻狀狆狌狋狊犻犵狀犪犾，狊狅狋犺犲狀狅犻狊犲犪狋犳狉犲狇狌犲狀犮犻犲狊 犳犔犗±犳犐犉，３犳犔犗 ±犳犐犉，５犳犔犗 ±犳犐犉 …犻狊犱狅狑狀犮狅狀狏犲狉狋犲犱狋狅 犐犉犪狋狅狌狋狆狌狋，犻狀狋犺犲狊犪犿犲狑犪狔犪狊狋犺犲犻狀狆狌狋狊犻犵狀犪犾［６］ ． 犜犺狌狊，狋犺犲狋狉犪狀狊犮狅狀犱狌犮狋狅狉狊狋犪犵犲犮狅狀狋狉犻犫狌狋犲狊狅狀犾狔狑犺犻狋犲 狀狅犻狊犲狋狅狋犺犲狅狌狋狆狌狋狀狅犻狊犲犻犳狋犺犲狊狑犻狋犮犺犻狀犵狋狉犪狀狊犻狊狋狅狉狊 １１３０