Question E4D11:
Why are odd-order intermodulation products, created within a receiver, of particular interest compared to other products?  

Choices:  
A: Odd-order products of two signals in the band being received are also likely to be within the band  
B: Odd-order products are more likely to overload the IF filters  
C: Odd-order products are an indication of poor image rejection  
D: Odd-order intermodulation produces three products for every input signal within the band of interest    

Correct Answer is  A: Odd-order products of two signals in the band being received are also likely to be within the band  

To see why odd-order intermodulation (IMD) is especially troublesome, remember that nonlinear stages create spurious signals at combinations of the input frequencies.

Why the correct answer is correct (A)
- Intermod products from two signals at $f_1$ and $f_2$ occur at
  $$f_{\text{IMD}} = m f_1 \pm n f_2,\quad \text{with } m+n = N \text{ (order)}.$$
- For odd orders (especially 3rd order), the products land near the original signals. For two close in-band signals:
  - 3rd-order products: $2f_1 - f_2$ and $2f_2 - f_1$.
  - Let $f_c = (f_1+f_2)/2$ and $\Delta = f_2 - f_1$. Then
    $$2f_2 - f_1 = f_c + \tfrac{3}{2}\Delta,\quad 2f_1 - f_2 = f_c - \tfrac{3}{2}\Delta.$$
  - These stay inside or near the received band, so you hear them as false in-band signals.

Why the other choices are incorrect
- B: “Odd-order products are more likely to overload the IF filters”
  - Filters don’t “overload” in this sense; nonlinear stages (RF/IF amps, mixer) overload and create IMD. Filters may pass or reject products, but they aren’t the stage that overloads.
- C: “Odd-order products are an indication of poor image rejection”
  - Image responses are due to mixer frequency conversion (LO ± IF), not intermodulation. Poor image rejection is a separate issue from IMD.
- D: “Odd-order intermod produces three products for every input signal”
  - Not true. With two tones, 3rd-order IMD produces two close-in products ($2f_1-f_2$, $2f_2-f_1$). The count is not “three per signal,” and depends on order and tone combinations.

Useful formulas and rules of thumb
- General IMD frequencies:
  $$f_{\text{IMD}} = m f_1 \pm n f_2,\quad m+n=N.$$
- 2nd order (even): $f_1+f_2$ (often far above band), $|f_1-f_2|$ (near DC for close tones); typically easier to filter or reject with balanced mixers.
- 3rd order (odd): $2f_1-f_2$, $2f_2-f_1$ (fall near the originals, hence in-band).
- Receiver linearity metric: third-order intercept point (IP3). Higher IP3 ⇒ better resistance to in-band IMD.