Conversion gain for mixer (BJT switch)

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SUMMARY

The discussion focuses on calculating the conversion gain for a BJT mixer connected to a 50Ω resistor, with a derived conversion gain of 12.25. The Third Order Intercept Point (IIP3) is given as 15 dBm, leading to the need for calculating A1dB using the formula A1dB = √[0.145|α1/α3|]. Additionally, P1dB is calculated using P1dB = A1dB²/(2RL). The conversation highlights challenges in understanding the alpha parameters related to transistor current gains.

PREREQUISITES
  • Understanding of BJT (Bipolar Junction Transistor) operation
  • Familiarity with conversion gain calculations in RF circuits
  • Knowledge of IIP3 (Third Order Intercept Point) and its significance
  • Basic grasp of electrical engineering principles, particularly in relation to resistive loads
NEXT STEPS
  • Research the derivation of the conversion gain formula for BJT mixers
  • Learn about the significance and calculation of A1dB in RF applications
  • Investigate the relationship between alpha parameters and transistor performance
  • Study the implications of P1dB in amplifier design and performance metrics
USEFUL FOR

Electrical engineers, RF circuit designers, and students studying microwave engineering who are looking to deepen their understanding of mixer performance and gain calculations.

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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