1. 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

2. 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

3. 3 Balanced modulator mixers

4. 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

5. 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)

6. 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

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

8. 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

9. 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

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

11. 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

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

13. 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

14. 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

15. 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

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

17. 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

18. 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

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

20. 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

21. 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

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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. FET Mixers 33

34. 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

35. 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

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

37. 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

38. 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

39. 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

40. 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

41. 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