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Chapter 6 Mixers

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Chapter 6 Mixers Chapter 6 Mixers 1 Sections to be covered • 6.1 General Considerations • 6.2 Passive Downconversion Mixers • 6.3 Active Downconversion Mixers 2 Chapter Outline General Passive Mixers Considerations Conversion Gain Port-to-Port Feedthrough Single-Balanced and Double-Balanced Mixers Passive and Active Mixers Active Mixers Conversion Gain 3 Recall: Generic TX & RX 4 General Considerations (I) Mixers perform frequency translation by multiplying two waveforms. Example: mixer using an ideal switch VLO turns the switch on and off, yielding VVIF RFor V IF 0 multiplication of the RF input by a square wave toggling between 0 and 1, even if VLO is a sinusoid. ⋅ 5 General Considerations (II) Mixers perform frequency translation by multiplying two waveforms (and possibly their harmonics). Example: mixer using an ideal switch ⋅ VRF The circuits mixes the RF input with all of the LO harmonics, producing “mixing spurs”. The LO port of this mixer is very nonlinear. The RF port must remain sufficiently linear to satisfy the compression and intermodulation requirements. 6 Performance Parameters: Port-to-Port Feedthrough feedthrough from the LO port to the RF and IF ports. gate-source capacitances gate-drain capacitances Owing to device capacitances, mixers suffer from unwanted coupling (feedthrough) from one port to another. Example of LO-RF Feedthrough in Mixer Consider the mixer shown below, where VLO = V1 cos ωLOt + V0 and CGS denotes the gate-source overlap capacitance of M1. Neglecting the on-resistance of M1 and assuming abrupt switching, determine the dc offset at the output for RS = 0 and RS > 0. Assume RL >> RS. The LO leakage to node X is expressed as Basic component of VLO (square wave) can be expressed as The dc component： 8 The output dc offset vanishes if RS = 0. Single-Balanced Mixers The simple mixer operate with a single-ended RF input and a single-ended LO. Discarding the RF signal for half of the LO Single-balanced mixer: Two switches are driven by differential LO phases; transform the RF input to the two outputs. 1cos 0 significant 0cos 0 1 cos 0 LO-IF feedthrough!!!! 1 2 1 cos 0 1 cos 2 4 1 cos ,,,..., ⋅ 1 2 cos 2 2 ⋅ cos 3 ... 4 4 3 cos cos 3 3 . The circuit provides differential outputs easing the design of subsequent stages. 9 The LO-RF feedthrough at ωLO (dc component) vanishes if the circuit is symmetric due to the differential output. Single-Balanced Mixers The simple mixer operate with a single-ended RF input and a single-ended LO. Discarding the RF signal for half of the LO Single-balanced mixer: Two switches are driven by differential LO phases; transform the RF input to the two outputs. 1cos 0 0cos 0 1 2 1 cos 2 ⋅ 1 2 cos 2 2 cos 3 ... 3 The circuit provides differential outputs easing the design of subsequent stages. 10 The LO-RF feedthrough at ωLO (dc component) vanishes if the circuit is symmetric due to the differential output. Single-Balanced Mixers The simple mixer operate with a single-ended RF input and a single-ended LO. Discarding the RF signal for half of the LO Single-balanced mixer: Two switches are driven by differential LO phases; transform the RF input to the two outputs. 1cos 0 1 cos 0 significant 0cos 0 1 cos 0 LO-IF feedthrough!!!! 1 2 1 cos 2 4 1 cos ,,,..., ⋅ 1 2 cos 2 2 ⋅ cos 3 ... 4 4 3 cos cos 3 3 . The circuit provides differential outputs easing the design of subsequent stages. 11 The LO-RF feedthrough at ωLO (dc component) vanishes if the circuit is symmetric due to the differential output. LO-RF/LO-IF Feedthrough in Direct-Conversion RX In the direct-conversion receiver: LO-RF feedthrough is entirely determined by the symmetry of the mixer circuit and LO waveforms. (cancelled by balance structure) The LO-IF feedthrough is not harmful because it is heavily suppressed by 12 the baseband low-pass filter(s). Power of RF signal is smaller than that of LO, which makes LO-RF feedthrough more harmful. RF-IF/RF-LO Feedthrough in Direct-Conversion RX RF frequency is equal to LO frequency. A large in-band interferer can couple to the LO and injection-pull it. Effect? corrupting the LO spectrum. Solution? interpose a buffer between the LO and the mixer The RF-IF feedthrough corrupts the baseband signal by the beat component 2 resulting from even-order distortion in the RF path. (cos ωRFt related to IP2, but not discussed in this course) 13 LO-RF/LO-IF Feedthrough in Heterodyne RX Special case: LO frequency is far away from RF frequency while close to IF frequency. The LO-RF feedthrough is relatively unimportant The LO leakage falls outside the band Attenuated by the selectivity of the LNA, the front-end band-select filter, and the antenna. Even there is residual LO leakage the dc offset appearing at the output of the RF mixer It can be removed by a high-pass filter (due to the IF output). The LO-IF feedthrough becomes serious if ωIF and ωLO are too close, We can not remove ωLO by filtering. LO is generated locally, with a high power level; LO feedthrough may desensitize the IF mixers if its level is comparable with their 1-db compression point. 14 Double-Balanced Mixers The single-balanced mixer We connect two single-balanced mixers suffers from significant LO- their output LO feedthroughs cancel， IF feedthrough. but their output signals do not. 1 cos 0 1 cos 0 4 1 cos ,,,..., ⋅ 4 cos 4 cos 3 3 . 2 ⋅ 8 8 cos cos 3 3 . 15 The circuit operates with both balanced LO waveforms and balanced RF inputs. Double-Balanced Mixers The single-balanced mixer We connect two single-balanced mixers suffers from significant LO- their output LO feedthroughs cancel， IF feedthrough. but their output signals do not. 1cosLOt 0 St2 ()LO 1cosLOt 0 n1 2 4 (1) cosntLO n1,3,5,..., n vtout() vtS RF ()2 ( LO t ) 4 vt()cos t RF LO 4 vt()cos3 t 3 RF LO ... 16 Double-Balanced Mixers The single-balanced mixer We connect two single-balanced mixers suffers from significant LO- their output LO feedthroughs cancel， IF feedthrough. but their output signals do not. 1cosLOt 0 St2 ()LO 1cosLOt 0 n1 2 4 (1) cosntLO n1,3,5,..., n vtout() vtS RF ()2 ( LO t ) 4 vt()cos t RF LO 4 vt()cos3 t 3 RF LO ... vtout() vtvt out () out () 2 vtS RF () 2 ( LO t ) 88 vt()cos t vt ()cos3 t RF LO3 RF LO ... 17 The circuit operates with both balanced LO waveforms and balanced RF inputs. Effect of Feedthrough Direct-Conversion Heterodyne LO-RF Harmful, Harmless DC component LO-IF Harmless Harmful, Desensitization RF-LO Harmful, Large interferer, Harmless Injection-pull RF-IF Harmless Harmless IF-LO Harmless Harmful, Oscillator pulling IF-RF Harmless Harmless 18 Passive and Active mixers Mixers can be broadly classified into “passive” and “active” topologies; As to a passive mixer, its transistors do not operate as amplifying devices. Each type can be realized as a single-balanced or a double- balanced circuit. 19 Passive Downconversion Mixers: Gain The input is multiplied by a square wave toggling between 0 and 1. The first harmonic has a peak amplitude of 2/ π and can be expressed as (2/ π) cosωLOt. The convolution of an RF signal with these impulses creates the IF signal with a gain of 1/ π (≈-10 dB). The conversion gain is equal to 1/π for abrupt LO switching. 1cosLOt 0 St1()LO 0cosLOt 0 n1 122 (1) cosntLO 2 n1 n vtIF() v RF () tS1 ( LO t ) 12 2 vt() vt ()cos t vt ()cos3 t ... 23RF RF LO RF LO We call this topology a “return-to-zero” (RZ) mixer because the output falls20 to zero when the switch turns off. Example of Downconversion Gain of Single- Balanced Topology Determine the conversion gain if the circuit is converted to a single-balanced topology. 1 cos 0 4 1 cos 1 cos 0 Solution: ,,,..., 4 4 ⋅ cos cos 3 . 3 The second output is similar to the first but shifted by 180 °. The differential output contains twice the amplitude of each single-ended output. The conversion gain is equal to 2/π (≈ -4 dB). 21 Providing differential outputs and twice the gain, this circuit is superior to the single- ended topology. Example of Downconversion Gain of Double-Balanced Topology Determine the voltage conversion gain of a double-balanced version. (Decompose the differential output to return-to-zero waveforms.) Solution: Solution: 88 vt() vtvt () () 2 vtS () ( t ) vt ()cos t vt ()cos3 t ... out out out RF2 LO RF LO3 RF LO Vout1 -Vout2 contains an IF amplitude of (1/π)(4V0). The peak differential input is equal to 2V0, the circuit provides a voltage conversion gain of 2/π, equal to that of the single-balanced counterpart. 22 Are there any ways to improve the gain? When the switch turns off, what can we do? 23 Sampling Mixer: the Idea If the resistor is replaced with a capacitor, such an arrangement operates as a sample-and-hold circuit and exhibits a higher gain because the output is held— rather than reset —when the switch turns off. The output waveform can be decomposed into waveforms. 24 Sampling Mixer: Conversion Gain Same as the switch The total IF output is therefore equal to If realized as a single-balanced topology, the circuit provides a gain twice this value, 1.186≈1.48dB about 5.5dB higher than its return-to-zero counterpart.
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