AC Circuit Analysis (3) Flashcards
How do Capacitors and Inductors behave at high and low frequencies?
High frequencies:
* Capacitor => like a short circuit, as impedence tends towards zero, this can be derived using transfer functions.
* Inductor => like an open circuit, impedence tends towards infinity, this can be derived using tansfer functions. Though makes sense since faradays law.
Low frequencies:
* Capacitor => like an open ciruict, impedence tends towards infinity, as it a physical gap that current or volts can’t cross (like in DC).
* Inductor =>like a short circuit, as impedence tends towards zero, as it is effectively just a coiled wire.
What do AC filters do?
They are used to attenuate (reduce) certain frequencies from a signal (i.e. low frequency noise or high frequency noise).
They reduce the amplitude of an AC voltage and the phase, but not the frequency.
- For example, A low pass filter shown below.
What is meant by transfer function, H(ω), for an AC filter?
This refers to almost the complex notation for gain. However it isn’t gain as gain uses real numbers and constants. This function varies with angular frequency. This can have real and imaginary numbers.
What is the transfer function and frequency response equations for a simple RC low-pass filter, as shown below?
Try to derive them to challenge yourself.
Note:
* Its easiest to think in terms of potential dividers for these filter circuits.
* see how gain is the modulus of both the complex numbers, (numerator and denomenator). The numerator is technically complex, just without any phase. See red.
What is the frequency response graphs, for a simple RC low pass filter?
Hint, think phase and gain (not in db)
What is the cut-off frequency or half-power frequency , ωc?
What about natural cut-off frequency?
- It is angular frequency where gain is equal to 1/root(2). This is the point where the power is halved, as shown in the bottom right below.
- Usually, this refers to the point where frequencies go from the passband to the stop band or vice versa.
- Natural cut-off frequency, fc = ωc/2π.
What is the equation for expressing gain in decibel, db, form?
Note:
* Vgain can just be written gain. It is just gain.
What would the bode plot of an RC low-pass filter frequency response look like?
Why are bode plots good?
- We plot angular frequency on the x-axis and gain (db) on the y-axis.
- Since we use gain(db) we can plot on a logarithmic graph, so we can see how the filter works over a much higher range of frequencies.
- see how at the cut-off frequency, when gain is -3db, the graph goes straight down at a certain slope. The slope refering to how much the frequency is attenuated over a given frequency range, usually a decade (a factor of 10)
What is the transfer function and frequency response of a simple RC high-pass filter, as shown below?
Note:
* Its easiest to think in terms of potential dividers for these filter circuits.
* see how gain is the modulus of both the complex numbers, (numerator and denomenator). The numerator is technically complex, just without any phase.
What is the frequency response graphs, for a simple RC high pass filter?
Hint, think phase and gain (not in db)
What does the impedence triangle look like for inductive loads? How can this be useful?
Note:
* See the triangle in the top left.
* For inductors, XL goes up 90 degrees to the resistive line.
* Remember impedence is the combined resistance and reactance in a load. So there may be resistance in an inductor, as shown on the left diagram.
* See how we can use this knowledge to simply add complex number to find out current or total voltage.
What does the impedence triangle look like for capacitive loads? How can this be useful?
Note:
* See the triangle in the top left.
* For inductors, XL goes down 90 degrees to the resistive line.
* Remember impedence is the combined resistance and reactance in a load. So there may be resistance in an capacitor, as shown on the left diagram.
* See how we can use this knowledge to simply add complex number to find out current or total voltage.
