Quick Summary: Always choose more capacitor values spread over a considerable range. Let the Equivalent Series Resistor (ESR) of capacitor be nominal (Not high, never too low). Place self resonating freq of caps closer.
Are capacitors with very low ESR figures beneficial?
No!. If ESR are very low, the impedance at minimum points decreases more (good!) and impedance at maximum points increases. The minimum and maximum points here refer to impedance curve. Hence, they are most of the time, not beneficial.
What happens when ESR goes low?
When ESR goes low, troughs get deeper and the peaks get higher.
Is minimum impedance is equal to ESR?
No. It will be lower than that.
At resonance, what is the impedance through the Capacitor?
The impedance across the capacitor will be equal to R. Resonance occurs, by definition, when imaginary part of the impedance equation is zero.
If i parallel 100 capacitors, what is its effect on self resonance frequency?
Paralleling capacitors doesn't change the self resonating frequency, but it effectively increases the capacitance, reduces inductance and reduces ESR.
What is the phase angle when resonance occurs?
Theoretically Zero
What is the anti resonance frequency point?
When a pair of capacitors are connected in parallel, there will be point on impedance plot between self resonating frequencies of both capacitors. The impedance will be significantly high compared to neighbor points. It's the point where one of the capacitor's reactance will be inductive and increasing and other's reactance will be capacitive and decreasing.
What will be the impedance at anti resonance frequency?
Impedance is given by Z = R/2 + square(X)/2R; it is very important to note that the relationship is inversely related. Hence, the point - if ESR is very low, then impedance grows huge at anti resonance frequency. The second term in the RHS grows big if R is very small.
For some reason if capacitors with very less ESR values have to be used what is the better choice?
Option rather than choice is to use too many capacitors. Only then a relatively flat impedance response can be achieved. But, the BOM cost increases. What here needs to be appreciated here is more number of capacitors are required only because of low ESR. Hence while choosing capacitors always goes for nominal ESR. Low ESR has more bad and less good in stores for us.
Note: It is instructive to place self resonant frequencies closer, which is achieved using capacitor of wide range.
How to calculate value of ceramic capacitors required to bring down input ripple to a nominal value?
Following formula can be used:
Iout x DC x (1-DC) x 1000
Cmin = ----------------------------------------- in uF
Fsw x Vp(max)
Fsw - Switching frequency
Iout - Steady load current
Cmin - Minimum required ceramic input capacitance
Vp(max) - Maximum allowed peak to peak ripple voltage
DC - Duty cycle = Vout / (Vin x n); n - Efficiency
Why are ceramic capacitors are placed next to tantalum capacitors at the input of switching regulators?
The extreme low ESR values of ceramic capacitors reduces ripple voltage significantly. Electrolytic capacitors are bulky and ESR figures are high and hence fails to reduce ripple effectively.
Also the large ESR values of tantalum capacitors leads to huge power dissipation because of higher ESR compared to ceramic.
How to calculate required value of bulk capacitor at input of switching regulator?
Following formula can be used:
1.21 x (Itr) x (Itr) x L
Cmin = ------------------------------------- in uF
delV x delV
Itr- Transient current
L - Value of filter(Inductor) in series at input voltage; if not populated a nominal value of 40 - 50 nH can be assumed which is parasitic inductance of trace and routing from host supply.
delV - Maximum allowable dip during peak transient step.
Comment on output capacitor selection for switching regulators
- External capacitors are required to achieve fast response to load transients
- Local decapacitors should be used to insure high frequency load regulation at point of load
- Low value of ceramic can be used abundantly
- Low ESR caps are recommended
- Impedance of the output capacitance affects the damping of the output filter
What is self resonant frequency of a capacitor?
For a given capacitor, self resonance frequency is the maximum frequency until which capacitor is usable. The Equivalent series Inductance (ESL) of capacitor dominates after this point.
The self resonance frequency of ceramic capacitor increases by a factor of 3.16 for every 10 times decrease in the capacitor value.
Please share your opinion in the comments box below.
Source: White paper on Selection of Bypass caps for Decoupling by Douglas G Brooks