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The following is differential pair small signal analysis from the book Design of Analog CMOS Integrated Circuits.

Let us set \$V_{in2}\$ to zero and find the effect of Vin1 at X and Y [Fig. 4.17(a)]. To obtain \$V_X\$ , we note that M1 forms a common-source stage with a degeneration resistance equal to the impedance seen looking into the source of M2 [Fig. 4.17(b)]. Neglecting channel-length modulation and body effect, we have \$R_S = 1/g_{m2}\$ The following is analysis of differential pairs. How can this circuit remove \$R_{D2}\$ in (c)?

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This is what I thought about

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  • \$\begingroup\$ Can you explain to us why do you think that you should include the Rd2 resistor? Notice that in this case, M2 is working as a common-gate amplifier. What is Rin of a CG stage? \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 13:23
  • \$\begingroup\$ @G36 M2 is seen as a resistor \$R_S\$. Which transistor of \$R_{in}\$ you are talking about? \$\endgroup\$
    – kile
    Commented Nov 30, 2023 at 14:30
  • \$\begingroup\$ Yes, M2 is seen as a resistor Rs. This Rs resistance is equal to the input resistance of a CG stage. Because in this case M2 is working as a common-gate amplifier. \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 14:54
  • \$\begingroup\$ @G36 M2 is in series with \$R_{D2}\$. Why should we remove \$R_{D2}\$? \$\endgroup\$
    – kile
    Commented Nov 30, 2023 at 14:56
  • \$\begingroup\$ Find Rin of a CG state (also do not forget to neglect channel-length modulation) and you will see why. Or try to find Rin in a circuit that contains an ideal current source in series with a resistor. And you will see that a series resistor does not influence the current. \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 15:03

1 Answer 1

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The following is Thevenin analysis.

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$$g_m V_T = I_T$$

$$\frac{V_T} {I_T} = 1 / g_m$$

For Thevenin voltage

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$$V_{eq} = V_T$$ $$g_m (V_T- V_{eq}) = 0$$ So current source is zero.

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  • \$\begingroup\$ So, do you see now why we do not include Rd2 in Rin equation? \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 15:33
  • \$\begingroup\$ @G36 Thank you. Is Thevenin \$V_{eq}\$ same as \$V_{in}\$? \$\endgroup\$
    – kile
    Commented Nov 30, 2023 at 15:35
  • \$\begingroup\$ To be honest I do not understand what you are trying to achieve involving thevenin's voltage here. For what purpose. \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 15:38
  • \$\begingroup\$ @G36 In last example we have to calculate Veq electronics.stackexchange.com/questions/691011/… \$\endgroup\$
    – kile
    Commented Nov 30, 2023 at 15:40
  • \$\begingroup\$ But we do not have to do it here because Vin2 = 0V (M2 gate is at AC GND). \$\endgroup\$
    – G36
    Commented Nov 30, 2023 at 15:43

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