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LW1DSE > TECH 14.07.12 19:11l 114 Lines 4642 Bytes #999 (0) @ WW
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Subj: Dual Gate MOSFET Mixer (CP437)
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To : TECH@WW
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MIXING MODES
============
Mixers can be classified as those which operate in a continuous
non-linear mode, or as those which operate in the switching mode.
A typical continuous non-linear mode mixer is the dual gate MosFET
circuit as illustrated in Figure 1. The MosFET has a square law characteris-
tic which is particularly good for mixing purposes. Because of its high gate
impedance, it requires little power to drive it and the separate gates provide
good isolation between the two signals being mixed.
Dual Gate MOSFET
LO IN .001 ΪΔΔΔΔΔΔΔΒΔΔΏ
³³ ³ ³ ³
OΔΔΔΔ΄ΓΔΔΔΔΒΔΔΔ¶ΔΔΩ ³ ³
³³ ³ ΗΔ<Ώ ³ ³ ΪΔΔΒΔΔΔΔΔΔO
OΔΔΏ ΪΔΔΒΔΔ(ΔΔΔ¶ΔΔ΄ ³ ³|³ ³
³ ³ ³ ³ ³ ³ Ϋ|Ϋ ³ Figure 1: Dual Gate MOSFET
³|³ ³ ³ ³ ΔΑΔ Ϋ|Ϋ ΔΑΔ mixer.
Ϋ|Ϋ ³ ±100kκ ΓΔΔΏ ΔΒΔ Ϋ|Ϋ ΔΒΔ FI OUT
Ϋ|Ϋ ΔΑΔ ± ³ ³ ³ Ϋ|Ϋ ³
Ϋ|Ϋ ΔΒΔ ± ± ³ ³ Ϋ|Ϋ ³
Ϋ|Ϋ ³ ± 220κ± ΔΑΔ ³ ³|³ ³
³|³ ³ ³ ± ΔΒΔ ³ ³ ΐΔΔΑΔΔΔΔΔΔO
³ ³ ³ ³ ± ³ ΐΔΔΕΔΔΔΔΏ
OΔΔΩ ΐΔΔΑΔΔ΄ ³ ³.047 ³ ³
³ ³ ³ ± ΔΑΔ
Signal IN ΐΔΔΔΔΔΔΕΔΔΩ ± ΔΒΔ .047
ΔΑΔ ± ³
/// 330κ ± ΔΑΔ
³ ///
O
VDD +9 to +12V
Most bipolar transistor and vacuum tube type mixers operate in the
continuous non linear mode. By comparison to the square law of the MOSFET,
the bipolar transistor and the semiconductor diode have an exponential cha-
racteristic and the vacuum tube a 3/2 power law.
The square law of the MosFET is good because harmonic generation is
theoretically limited to second order. This can be demontrated using another
common trigonometric identity:
2
cos(2A) = 1 - 2sin A
and
2
sin A = (1 + cos(2A) / 2
Hence, if we square an input component f, expressed as
Af sin(2γft)
we get:
2
Af sin(2γft) = Af [1 + cos(2γ2ft) / 2
We now have a frequency 2f (the second harmonic) but no other order
harmonics. It also means that in our square law mixer, higher order products
are limited to third order (2fo + fi) and (2fi + fo).
To make a comparison using the exponential law of the bipolar
transistor or diode, we can expand an exponential function using the Taylor
series:
x 2 3 4
e = 1 + x + x /2! + x /3! + x /4! etc.
If we put x = sin (2γft) we get terms containing the following:
2 3 4
sin(2γft), sin (2γft), sin (2γft), sin (2γft),...
and in fact, all powers of sin(2γft).
We have seen that sine squared component gives second harmonics, so
let us now examine sine cubed. For this, we use a third trigonometric
identity:
2
sin(3A) = 3sinA - 4sin 3A
Rearranging the form gives:
sin3A = (3/4)sinA - (1/4)sin(3A)
Putting 2γft = A, we get sin[3(2γft)] from within the sine cubed
term of the exponential function implying that a third harmonic is generated.
Without going any further with mathematics we might well predict
that a pattern follows in which each incremented power of sin(2γft)
produces a corresponding incremented order of harmonic. Assuming this to be
correct, a conclusion can be drawn that the exponential characteristic of the
bipolar transistor or semiconductor diode, generates all orders of harmonics.
compared with the square law of the MOSFET transistor which generates only
second harmonics.
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