10/28/2021 3D_4_Conversion Loss.docx 1/9 Jim Stiles The Univ. of Kansas Dept. of EECS Mixer Conversion Loss Again, a mixer/LO pair can be considered a two-port device. Now, let’s consider the “gain” of this 2-port device, i.e.:Mixer "Gain"IFout absRFinavlPPPP0Z 0ZIFabsPgVRFavlP10/28/2021 3D_4_Conversion Loss.docx 2/9 Jim Stiles The Univ. of Kansas Dept. of EECS Available power If the RF port of the mixer is reasonably matched, then total voltage is approximately equal the incident voltage on the RF port: ( ) ( )[ ]cosRF RF R R RFFFvt vt A tω φ+= = + And so, the available power of the “matched” source is: = =220082gRFRFavlVAPZZ 0Z 0Z gVRFavlP10/28/2021 3D_4_Conversion Loss.docx 3/9 Jim Stiles The Univ. of Kansas Dept. of EECS Absorbed power Likewise, the total down-converted signal voltage at the IF port is equal to the incident voltage on the “matched” load: ( ) ( )( )2c osLRFI OF RF RFIFωAtφπωvt vt+−+= = And so the power absorbed by the “matched” load is: 2220222IF RFRFabs avlAPPZ ππ = = 0Z 0Z IFabsPgV10/28/2021 3D_4_Conversion Loss.docx 4/9 Jim Stiles The Univ. of Kansas Dept. of EECS Mixer “gain” From this we conclude that the “gain” of an ideal balanced switching mixer is: 22240405Mixer "Gain".IFabsRFavlππPP= = ≅= In other words, the down-converted signal power is just 40.5% of the RF signal power! Or, when expressed with the decibel operator: = ≅−102410 3922log .IFabsRFavldBπPP And so, an ideal balanced mixer gain is about -3.922 dB.10/28/2021 3D_4_Conversion Loss.docx 5/9 Jim Stiles The Univ. of Kansas Dept. of EECS Conversion Loss Note that this mixer “gain” is less than one (i.e., less than 0 dB) so it actually represents a loss. Thus, mixers are not specified in terms of their gain, but instead in terms of their conversion loss: 10 10Conversion Loss 10log 10logIF RFabs avlRF IFavl absPPdBPP Note that conversion loss is simply the inverse of mixer gain, and thus we find that the ideal balanced mixer has a conversion loss of approximately 3.922 dB.10/28/2021 3D_4_Conversion Loss.docx 6/9 Jim Stiles The Univ. of Kansas Dept. of EECS Remember all those sinusoids! Q: I don’t understand. An ideal switch is lossless, so wouldn’t an ideal switching mixer exhibit no loss as well? A: Remember, there are more signals created at the IF port than just the down-converted term! I.E.,: ( )( )2cosIF RF RF LO RFn oddvt A ω nω t φπn∈= +−∑10/28/2021 3D_4_Conversion Loss.docx 7/9 Jim Stiles The Univ. of Kansas Dept. of EECS Another 40.5% is found! Recall that the two largest terms are for 1, 1n : ( )( ) ( )22cos cosRF LO RF LIF RF RF Oωω ωωvt V tφ V tφππ ≅ −+ + −− which are the down-converted (1n = −) and “up-converted” (1n = +) terms. This up-converted term (with frequency RF LOωω+) has the same conversion gain as the down-converted term: 22240405.IFupabsRFavlππPP= = ≅ In other words, the up-converted signal power is also just 40.5% of the RF signal power!10/28/2021 3D_4_Conversion Loss.docx 8/9 Jim Stiles The Univ. of Kansas Dept. of EECS 19% for the remaining sinusoids Together, these two signals (down-converted and up-converted) represent 81% of the RF signal power. The remaining 19% of the RF signal power is (at least ideally) distributed across the remaining IF signals (i.e., where n is odd and 3n ≥): ( )( )2cosIFn RF RF LO RFvt A ω nω t φπn= +−10/28/2021 3D_4_Conversion Loss.docx 9/9 Jim Stiles The Univ. of Kansas Dept. of EECS Conversion loss is bad Q: You keep using weasel words like “at least ideally”. Should I then infer that the conversion loss of a real balanced mixer is actually not 3.922 dB? A: That is correct! Due to a number of issues (e.g. poor port-matching, lossy devices, spurious signal creation, imperfect switching characteristics), the conversion loss of a “real” mixer will be greater than the ideal. The conversion loss of actual balanced mixers will typically range from 4.0 dB to 10.0 dB. You should select a mixer with as low a conversion loss as
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