You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
51 lines
1.6 KiB
51 lines
1.6 KiB
id: fund-ex-02a
|
|
type: design
|
|
difficulty: easy
|
|
points: 10
|
|
related_lesson: fund-02
|
|
question: |
|
|
Draw the circuit for a spark with the following parameters:
|
|
- Spark length: L = 5 feet
|
|
- Mutual capacitance: C_mut = 12 pF (from FEMM)
|
|
- Plasma resistance: R = 50 kΩ
|
|
|
|
Label all component values including the shunt capacitance C_sh.
|
|
|
|
hints:
|
|
- "Use the empirical rule: C_sh ≈ 2 pF/foot"
|
|
- "The topology is (R || C_mut) in series with C_sh"
|
|
- "Draw from topload terminal to ground reference"
|
|
|
|
solution:
|
|
steps:
|
|
- "Calculate C_sh using empirical rule: C_sh = 2 pF/foot × 5 feet = 10 pF"
|
|
- "Draw topload at top as measurement terminal"
|
|
- "Draw C_mut in series from topload"
|
|
- "At node connecting C_mut, draw R and C_sh in parallel to ground"
|
|
- "Alternative: Show R || C_mut as parallel combination, then C_sh in series to ground"
|
|
|
|
answer: |
|
|
Circuit diagram:
|
|
Topload (V_top)
|
|
|
|
|
[C_mut = 12 pF]
|
|
|
|
|
+----------- Node_spark
|
|
| |
|
|
[R = 50 kΩ] [C_sh = 10 pF]
|
|
| |
|
|
GND --------- GND
|
|
|
|
component_values:
|
|
C_mut: "12 pF"
|
|
C_sh: "10 pF"
|
|
R: "50 kΩ"
|
|
|
|
explanation: |
|
|
The spark circuit model uses three components: C_mut couples the topload to the
|
|
spark channel, R represents plasma resistance where power is dissipated, and C_sh
|
|
provides the shunt capacitance to ground. The empirical 2 pF/foot rule gives a
|
|
good estimate for C_sh, which for a 5-foot spark yields 10 pF. This topology
|
|
ensures current through R must also flow through either C_mut or C_sh.
|
|
|
|
related_concepts: ["circuit-topology", "lumped-model", "C_sh-empirical-rule", "spark-capacitance"]
|