Conversion gain for mixer (BJT switch)

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Discussion Overview

The discussion revolves around the conversion gain for a mixer using a BJT switch, focusing on specific calculations related to the conversion gain, third-order intercept point (IIP3), and P1dB. Participants are addressing homework problems that involve theoretical and practical aspects of mixer performance.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states that the conversion gain can be calculated as 1/pi = 0.318.
  • Another participant expresses confusion regarding the alphas mentioned in the formula, suggesting they might relate to the collector-emitter current gains of the transistors.
  • A different participant proposes a formula for part (a) as (1/pi)*g_m*R1, calculating it to be approximately 12.25 for conversion gain.
  • There is mention of searching for a derivation of the formula related to alphas, indicating a need for further clarification.
  • One participant notes that the IIP3 is likely in the millivolts range but does not provide a definitive value.
  • Another participant shares their experience of searching for relevant datasheets and expresses frustration over not finding useful results.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the interpretation of the alphas or the specific values for IIP3 and P1dB. Multiple competing views and uncertainties remain regarding the calculations and the underlying principles.

Contextual Notes

Participants have not fully resolved the definitions and implications of the alphas in the context of the formulas provided. There are also unresolved mathematical steps related to the calculations for A1dB and P1dB.

Who May Find This Useful

This discussion may be useful for students or professionals interested in RF engineering, specifically those working with mixers and BJT switches in practical applications.

adamaero
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Homework Statement


a) If this mixer is connected to a matching 50Ω resistor, what is the conversion gain?
b) IIP3 (Third Order Intercept Point) is 15 dBm, what would be A1dB?
c) What is P1dB?

Homework Equations


V90MWI7.png

https://www.ece.ucsb.edu/Faculty/rodwell/Classes/ece218b/notes/Mixer1.pdf#page=9

b) A1dB = √[0.145|α13|]

c) P1dB = A1dB2/(2RL)

The Attempt at a Solution



a) 1/pi = 0.318

b) I don't understand the alphas.
 

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adamaero said:
b) I don't understand the alphas.
Perhaps they might be associated with the collector-emitter current gains of the transistors?

You might need to search out a derivation of that formula.
 
Searching "-datasheet transistor 1db gain .045" doesn't help.
 
Where did you first come across the formula?
 
OCyUttH.png
 

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Part (a) is
(1/pi)*g_m*R1
(1/pi)*(1/26)*1000 = 12.25 = C.G.

(b) probably in millivolts range

Re-did search with "-datasheet transistor 1db gain" and got some good results... But never mind; I'll move on, sunk cost.
 

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