Decibel Scale Reminder

1
Decibel Scale Reminder
Voltage gain
2
1st Order RC Low-Pass Filter
Poor high frequency suppression.
Try 2 stages
3
2nd Order RC Low-Pass Filter
Steeper high frequency slope at the expense of
increased attenuation at the corner frequency.
4
2nd Order RLC Low-Pass Filter
2nd order high frequency slope with an ability to
adjust attenuation/gain at the corner frequency
independently via Q.
5
Gain Greater Than 1?

• Question
• RLC circuit is a passive circuit with no active
  elements (i.e., amplifiers.) How can it have a
  gain greater than 1?
• Answer
• First note that we are considering voltage gain
  and not the power gain. Indeed, the power gain
  can never exceed 1 for a passive circuit.
• Second, note that a transformer is also a passive
  circuit element and it does produce higher
  voltage at the output if the number of secondary
  turns is higher than the number of primary turns.
  
• An RLC circuit amplifies the voltage by a factor
  of Q at resonance because, when the reactances of
  the inductor and the capacitor cancel, a large
  current flows thru a large reactance.

Consider an example
6
Series Resonance Example
At resonance, only small R limits the current, so
current is large (1Amp.) However, although the
reactances of the capacitor and the inductor
cancel, they are still individually large (Q
times larger than R.) Consequently, voltage drop
across the inductor and the capacitor is Q100
times greater than the source voltage! This is
true only in the vicinity of resonance whose
bandwidth relative to the resonant frequency is
approximately 1/Q1.
7
1st and 2nd Order Low Pass Compared
1st order RC
2nd order RC
RLC (Q1)
8
Assignments

• READING
• Sec. 3.4 (only The Low-Pass Response)