Question E4D08:
What causes intermodulation in an electronic circuit?  

Choices:  
A: Negative feedback  
B: Lack of neutralization  
C: Nonlinear circuits or devices  
D: Positive feedback    

Correct Answer is  C: Nonlinear circuits or devices  

Correct answer: C — Nonlinear circuits or devices

Why C is correct:
- Intermodulation distortion (IMD) occurs when a device’s transfer function is nonlinear. If the input is the sum of two tones, $v(t) = A_1 \cos(2\pi f_1 t) + A_2 \cos(2\pi f_2 t)$, and the device has a polynomial response:
  $$v_{\text{out}} = a_1 v + a_2 v^2 + a_3 v^3 + \dots,$$
  the squared and cubed terms create products at new frequencies (sums and differences), i.e., mixing products.
- These intermod products appear at:
  - Second order: $f_{IM2} = f_1 \pm f_2,\ 2f_1,\ 2f_2$
  - Third order: $f_{IM3} = 2f_1 \pm f_2,\ 2f_2 \pm f_1$
- Third-order products are the most troublesome in receivers because they fall near the desired signals.

Why the others are incorrect:
- A: Negative feedback reduces nonlinearity and thus reduces IMD; it does not cause intermodulation.
- B: Lack of neutralization refers to uncontrolled feedback in certain RF amplifiers (e.g., tubes) that can lead to oscillation. While oscillation is bad, the root cause of intermodulation is nonlinearity, not the absence of neutralization itself.
- D: Positive feedback promotes oscillation or regeneration. It can make a circuit unstable, but intermod products still require a nonlinear element; positive feedback alone does not create IMD.

Useful formulas and rules of thumb:
- Third-order intermod levels grow 3 dB for each 1 dB increase in input; fundamentals grow 1 dB per 1 dB.  
- Third-Order Intercept Point (IP3): a figure of merit for linearity. Higher IP3 ⇒ better IMD performance.  
- Common third-order IMD tones to watch: $2f_1 - f_2$ and $2f_2 - f_1$.