So, after foolishly thinking I knew all about poles and zeroes of transfer functions after a few lectures on it, we're given this problem:
Firstly, I didn't know that a transfer function could be between a current quantity and a voltage quantity - I thought it was a ratio between two relative quantities, such as input voltage and output voltage. This just looks like an impedance, relating voltage to current.
Still, I made an attempt an attempt at the problem - I felt that it was just a simple case of applying Ohm's law to the total impedance, so V = iZ:
However, as you can see, doing this I get a real zero, and two complex poles. While the question doesn't ask us to explain them, I can't seem to work out how these values are related to the input frequency. It just seems wrong, somehow.
We were told in the lecture that, if a zero has a value s=X, then at frequency X Hz, there will be a +20db/decade slope. Likewise, a pole with a value s=X will have a -20db/decade slope at X Hz. These combine together to give the bode plot of the transfer function.
However, to me, this seems to imply that all the values of s will be real - what happens if a pole or zero value has an imaginary part?
Or have I gone about this in completely the wrong way? I also had a go at writing differential equations, but I couldn't really find one that applied.
If anyone has the time, please post how you would do it, or let me know if/where I'm going wrong. Please remember that I'm a simple student and can only do it using impedance functions or differential equations and the Laplace transform!
Thanks very much for anything you can do to help me fully understand this!
Ben
Firstly, I didn't know that a transfer function could be between a current quantity and a voltage quantity - I thought it was a ratio between two relative quantities, such as input voltage and output voltage. This just looks like an impedance, relating voltage to current.
Still, I made an attempt an attempt at the problem - I felt that it was just a simple case of applying Ohm's law to the total impedance, so V = iZ:
However, as you can see, doing this I get a real zero, and two complex poles. While the question doesn't ask us to explain them, I can't seem to work out how these values are related to the input frequency. It just seems wrong, somehow.
We were told in the lecture that, if a zero has a value s=X, then at frequency X Hz, there will be a +20db/decade slope. Likewise, a pole with a value s=X will have a -20db/decade slope at X Hz. These combine together to give the bode plot of the transfer function.
However, to me, this seems to imply that all the values of s will be real - what happens if a pole or zero value has an imaginary part?
Or have I gone about this in completely the wrong way? I also had a go at writing differential equations, but I couldn't really find one that applied.
If anyone has the time, please post how you would do it, or let me know if/where I'm going wrong. Please remember that I'm a simple student and can only do it using impedance functions or differential equations and the Laplace transform!
Thanks very much for anything you can do to help me fully understand this!
Ben
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