Question E7C09:
What is a crystal lattice filter?  

Choices:  
A: A power supply filter made with interlaced quartz crystals  
B: An audio filter made with four quartz crystals that resonate at 1 kHz intervals  
C: A filter using lattice-shaped quartz crystals for high-Q performance  
D: A filter for low-level signals made using quartz crystals    

Correct Answer is  D: A filter for low-level signals made using quartz crystals  

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A crystal lattice filter is a narrowband RF/IF filter built from quartz crystals arranged in a bridge-lattice network. Because quartz crystals have very high $Q$ but limited power-handling, these filters are used at low signal levels (e.g., IF stages in receivers).

Why the correct answer is correct:
- “A filter for low-level signals made using quartz crystals” is correct because:
  - Quartz crystals provide very high $Q$ and steep skirts, ideal for narrow IF passbands.
  - The lattice topology (a bridge network of crystals, often four) yields good selectivity and symmetry.
  - Crystals can be damaged or exhibit nonlinearity at higher power; thus they are used at low levels.

Why the other choices are incorrect:
- A: “A power supply filter made with interlaced quartz crystals”
  - Quartz crystals are RF resonators, not used for 50/60 Hz power-supply filtering and cannot handle that power.
- B: “An audio filter made with four quartz crystals that resonate at 1 kHz intervals”
  - Quartz crystals resonate at RF (kHz–MHz), not at audio frequencies; “1 kHz intervals” is not what defines a lattice filter.
- C: “A filter using lattice-shaped quartz crystals for high-Q performance”
  - “Lattice” refers to the circuit configuration (bridge network), not the physical shape of the crystals.

Useful formulas and rules of thumb:
- High selectivity from high $Q$:
  $$Q = \frac{f_0}{\text{BW}}$$
  Example: for a 9 MHz IF SSB filter with 2.4 kHz BW, $Q \approx \frac{9\times10^6}{2.4\times10^3} \approx 3750$ (effective system $Q$; individual crystals can have $Q \sim 10^4$–$10^5$).
- Crystal resonances:
  - Series resonance at $f_s$; parallel (antiresonance) at $f_p$.
  - Approximate separation:
    $$f_p \approx f_s\sqrt{1 + \frac{C_m}{C_0}} \approx f_s\left(1 + \frac{C_m}{2C_0}\right)$$
    where $C_m$ is motional capacitance and $C_0$ is shunt capacitance.
- Practical notes:
  - Typical use: IF filters (e.g., 9 MHz, 10.7 MHz) for CW/SSB/digital modes.
  - Typical insertion loss a few dB; power handling is low (small-signal only).

In short: a crystal lattice filter is a low-level, very selective IF filter that uses quartz crystals in a lattice (bridge) network.