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1 Mixers Mixers plays an important role in both the transmitter and the receiver Mixers are used for down frequency conversion in the receiver Mixers are used for up frequency conversion in the transmitter Mixers can be implemented with many different circuits Some of the widely used mixer circuits will be discussed in the next few lectures

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2 Popular mixers Some of the popular mixer circuits are The diode mixers 1.Balanced diode mixer 2.Switching diode mixer 3.Ring diode mixer 4.Square law mixers Transistor mixers this can be designed using either FET or BJT transistors Gilbert cell mixer

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3 Balanced modulator mixers

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4 Analysis of balanced modulator mixer Consider the information signal f(t) applied to the input of the center tapped transformer Consider carrier signal is cosω c t is applied to the second transformer The voltage applied to the input of the upper diode is The voltage applied to the input of the lower diode is

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5 Analysis of balanced modulator mixer If the currents leaving from both diodes are expanded using the first two terms of the Taylor series expansion, we may got the following two equations From circuit shown in slide 3 the output voltage is given by (1) (2) (3)

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6 Analysis of balanced modulator mixer If we substitute equations (1) and (2) in (3) the output voltage then can be written as Since f(t) is a low frequency signal then, it can be filtered out by the band pass filter attached at the end terminal of the circuit

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7 Switching type mixer A four diode switching type mixer is shown below

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8 Switching type mixer If the local oscillator voltage V Lo is positive, then diodes D 2 and D 3 will conduct The resulting equivalent circuit is shown in the next figure

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9 Switching type mixer The previous circuit can be redrawn as shown By writing KVL for the upper and lower loops we my get the following two equations

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10 Switching type mixer The local oscillator voltage can be eliminated by the addition of the above two equations Note that or

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11 Switching type mixer When the V Lo reverse its polarity diodes D 1 and D 4 will conduct The resulting circuit can be redrawn again as shown in the next slide

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Switching type mixer If similar analysis is performed on this circuit we got 12

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Switching type mixer The mixer output voltage is proportional to the input voltage and switched positively or negatively at the local oscillator frequency This means that the output voltage is multiplied by a square wave The resulting voltage at the output of the mixer can be mathematically expressed by 13

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Switching type mixer The local oscillator signal can be viewed as a square wave as shown below Recall that the Fourier transform of the square wave is given by Assume also the input voltage is given by 14

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Switching type mixer The voltage measured at the mixer output is given by The above equation shows that the message signal is located at odd multiple n of the carrier 15

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Diode ring mixer Another type of diode mixer is the diode ring mixer which is shown below 16

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Conversion loss The conversion loss is defined as the ratio of the output power in one sideband to signal input power To illustrate this concept consider the following example 17

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Conversion loss example Example: Determine the conversion loss for the switching type diode mixer Solution: From the definition of the conversion loss we have to compute P in and P out in one of the side bands, then take their ratio 18

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Conversion loss example Solution: The input power can be determined from the inspection of the input section of the mixer circuit 19

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Conversion loss example Solution: Normally R L is much greater than r d /2, therefore The maximum input power is taken from the source when Under this condition The maximum input power is given by 20

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Conversion loss example Solution: From the output voltage equation the output voltage at either the upper or lower side band is given by The maximum output power is given by 21

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Conversion loss example Solution: The conversion loss is given by The conversion loss in dB is given by 22

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Distortion If the input signal power increases to levels larger than the local oscillator power distortion occurs and the response of the mixer became nonlinear as shown below 23

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Distortion At low input power levels, the power transfer is linear As the input power distortion begins and the response became non linear At high input power levels, the output saturates at a level proportional to the local oscillator power As the signal level increases further the intermodulation distortion (IMD) also increase 24

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Square law mixers The square law characteristics is approximated by several electronic devices The principle of operation of the square-law device is seen by the squaring the sum of two sine waves as indicated by the following equations 25

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Square law mixers A simple square law mixer is shown below At low frequency this kind mixers is not used because of the large conversion loss Transistor mixers are preferred because they can provide conversion gain 26

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BJT mixers A BJT transistor mixer is shown below The principle of operation of this mixer is based on the analysis of the collector current The collector current for V be >0 is given by and the emitter base voltage is given by 27

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BJT mixers If V be is substituted in the collector current, then If and, then the current can be expanded in a series of modified Bessel functions as Where and I n is the nth- order modified Bessel function 28

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BJT mixers The collector current consists of a DC component, components at both the input and local oscillator frequencies, components at the frequencies, and an infinite number of high frequency components The amplitude of either the upper or lower sideband components is given by 29

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BJT mixers the collector current will not vary with changes in the amplitude of the input signal if the local oscillator voltage amplitude is constant, and if V L >> V 1, since The mixer should have a linear response to changes in the input amplitude if The response will be within 2 percent of its linear response 30

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BJT mixers The ratio of the mixer response to the input signal amplitude is given by The amplitude of the side band current is 31

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FET Mixers The idealized FET current transfer characteristics is the square–law relation As can be seen from this relation the FET can be used as a mixer similar to diode An ideal FET mixer will not produce any third order intermodulation distortion 32

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FET Mixers 33

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FET Mixers Still, a properly biased and operated FET mixer will produce much smaller high-order mixing products than a bipolar transistor The FET also provides at least 10 times as great an input voltage range as the BJT If the drain current is in the constant current region and 34

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FET Mixers The drain current after expanding the drain current equation is given by The amplitude of the sum and difference frequencies is given by The term is referred as the conversion tranconductance g c 35

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FET Mixers Since for a JFET the transconductance is The conversion transconductance is one-fourth the small signal transconductance at V gs =0 36

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FET Mixer example Example: A given FET transistor with I DSS =40 mA and transconductance g m =14×10 -3 S at V gs =0 is to be used in a mixer. Estimate the conversion gain if a 50 Ω load is used Solution: The conversion gain is given by From the transconductance we can find v p as indicated 37

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FET Mixer example Solution: The local oscillator voltage should be kept to approximately 50 percent of this value in order to minimize distortion If V L =2.85 V, then the conversion transconductance is The magnitude of the voltage gain is 38

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Integrated circuit mixer (Gilbert cell) This kind of mixers uses some form of a variable transconductance multiplier This multiplier relies on the dependence of the transistor’s transconductance upon its bias current 39

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Integrated circuit mixer (Gilbert cell) The differential output voltage is given by The transconductance g m is given by Therefore, the output voltage V O is given by Which is the multiplication of the two signals 40

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Integrated circuit mixer (Gilbert cell) One difficulty with this circuit is that since the total current IE varies directly as a function of V2, a large common mode swing will occur This common mode swing can be removed by using the circuit shown below 41

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