Ideal mixers
	This is a modeling exercise. I wanted to understand better what are the differences between various mixer configurations.
	How much attenuation and how source resistance will change. I had a direct conversion SSB and CW receiver in mind when doing this.
	I modeled multiple mixer configurations with almost ideal switches. See the summary and its links below.
	Local oscillator signal was square wave and switches ideal relays with 1ohm on-resistance and 1megaohm off-resistance.
	Analog CMOS-switches today come close to these ideal switches except on-resistance is still higher.
	The results of each mixer  type are summarized on respective pages. I have listed
		change of source resistance, or mixer output resistance in comparison to RF generators source resistance
		mixer voltage gain when mixer load resistance is infinite
		total power gain, dB-sum of those two
	Summary
					Voltage gain		Change of source		Total power gain		Theoretical voltage
		Mixer configuration			infinite load resist.		resistance				gain, infinite load
				on/off-ratio	dB		multiplier	dB	dB		dB
		Clamp		50/50	-4.0		2	-3.1	-7.1		-3.922
		Serial		50/50	-4.0		2	-3.1	-7.1		-3.922
		Serial		25/75	-1.0		4	-6.1	-7.1		-0.912
		as a quadrature mixer		4 x 25/75	5.0	to I and Q	8	-9.1	-4.1	to I and Q	5.108
		Serial		12.5/87.5	-0.3		8	-9.1	-9.4		-0.224
		Push-pull		2 x 50/50	-3.9		1	-0.1	-4.0		-3.922
		as a quadrature mixer		4 x 25/75	5.0	to I and Q	8	-9.1	-4.1	to I and Q	5.108
		Doubler		2 x 50/50	2.1		4	-6.1	-4.0		2.098
		Doubler		2 x 25/75	5.1		8	-9.1	-4.1		5.108
		Doubler		2 x 12.5/87.5	5.8		16	-12.1	-6.4		5.796
	Conclusions
		Cutting LO duty cycle to half doubles mixer source (output) resistance.
		Shortening LO duty cycle increases voltage gain, mixer becomes more like a peak detector.
		Conversion gain of a mixer remains almost constant between 50/50 and 25/75 on/off-ratios.
		Therefore it is possible to get better conversion gain in a quadarature mixer than in basic mixer by combining
		the outputs in a proper way.
		In case of quadrature mixer, push-pull configuration do not provide any improvement over serial mixer.
	Voltage attenuation of serial switch mixer is defined by integral over switch on-time divided by on-time in radians.
	Calculations were done after the modeling and are shown on a separate page. The results are shown in the summary above.
	How much distortion then ? That was not analyzed here but could be another exercise some day..
	Pekka, OH1TV		24.12.2009
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