Day 25 Frequency Dependencec

We started the day with talking about frequency. The way a circuit behaves with the change in signal frequency if its frequency dependence behavior. In order to deal with frequency characteristics of a circuit we use transfer functions. Transfer functions is the circuits frequency-dependent ratio of the phasor output over the phasor input of current or voltage. We did an example in class below.

White board work of a transfer example. 1st step is to change to phasor domain, and then find the ratio of output and input, this particular case Io/Iin.

White board work continued, with S = jw. We then found the poles and zeros, the moment when s = 0.

We then wanted the plot and analyze the result. We first wrote Matlab code.

Picture of the Matlab code to print out the graph.

Another pitcure of the Matlab code, with the output of the transfer function, has a range where signal pass and after that linear part, the slopes approach zero.

We then move onto another example of a transfer function this time looking for H(w) = Vo/Vin.

White board work of the example, needed to transform to phasor domain, then use node analysis, and finally find zeros and poles.

Picture of the graph from the example, has a range of omega where the circuit behaves best.

One last exampe of transfer functions with H(w) = Vout/Vin.

White board work of the example. Again first step is to transform to phasor, and change jw  to S and find the roots of S.

We then talked about decibels scale and how they use the log base.

We then move onto the last lab of the class: Signals with Multiple Frequency Components

Prelab: 1)Draw circuit - picture below 2)Create signal sweep - picture below

Picture of the sweep function created.

Picture of the output, how the sweep looks like.

Picture of the real life circuit, R1 = 1k, R2 = 1K, C1 .47uF

White board of the prelab circuit. R1 = 1k, C1 = .47uF, signal going in order is: 500hz, 1k hz, and lastly 10k hz.

Picture of the first signal 500 hz.

Picture of the 500 hz signal. Blue is Vin, Yellow is Vout.

Picture of the data for the 500 hz signal. C1 = Vout, C2 = Vin. The signal is at 520 hz, Vinamp = 3.9 V, signal out is 525 hz, Voutamp = 976 mV, T = 1.9 ms. Hw = .976/3.9 = 0.25. The shape of the signal mimics the signal going in with "mini"signal on the line mimicking the signal in. A two order signal of two signals being mixed with the second  .25 smaller.

Picture of the second signal, 1k hz.

Picture of the 1k hz signal. Blue is Vin, Yellow is Vout.

Picture of the data for the 1k hz signal. C1 = Vout, C2 = Vin. The signal is at 1k hz, Vinamp = 3.73 V, signal out is 1k hz, Voutamp = 641 mV, T = 1 us. Hw = .641/3.7 = 0.173. The shape of the signal mimics the signal going in with "mini"signal on the line mimicking the signal in. A two order signal of two signals being mixed with the second  .173 smaller.

Picture of the third signal, 10k hz.

Picture of the 10k hz signal. Blue is Vin, Yellow is Vout.

Picture of the data for the 10k hz signal. C1 = Vout, C2 = Vin. The signal is at 10k hz, Vinamp = 3.87 V, signal out is 10k hz, Voutamp = 83 mV, T = 100 us. Hw = .83/3.78= 0.021. The shape of the signal mimics the signal going in with "mini"signal on the line mimicking the signal in.  Two signals being mixed with the second  .021 smaller. There is barely a Vout signal.

Second part of the lab with the sweeps, 100 hz signal going in.

Picture of the signal of the sweep going in.Vin = blue, Vout = yellow. High frequency low output, low frequency greater output.

Picture of the data for the 100 hz signal. C1 = Vout, C2 = Vin. The signal is at 100 hz, Vinamp = 3.36 V, signal out is 4.8 k hz, Voutamp = 809 mV, T = 3.4 ms. Hw = .89/3.33 = .264. Higher frequency Vout is very small, lower frequency Vout is closer to original in amplitude.

Picture of the sweep, 10 khz signal going in.

Picture of the signal of the sweep going in.Vin = blue, Vout = yellow. High frequency higher output, low frequency lower output.

Picture of the data for the 10k hz signal. C1 = Vout, C2 = Vin. The signal is at 10k hz, Vinamp = 3.39 V, signal out is 3.78 k hz, Voutamp = 474 mV, T = 411 us. Hw = .89/3.33 = .139. Higher frequency Vout is very small, lower frequency Vout is closer to original in amplitude.

Conclusion of the lab: The vout/vin in relation to the signal frequency of 500, 1k and 10k hz signal show a steady decrease, which matched our prediction of higher frequency lower output. The interesting part was with the signal mixing the signal out matched the signal in with its own signal on top of the signal out. It would have two signals in one. For the sweep signal 1k and 10k hz signal, it went from the signal source of small Vout to big Vout for the 1k signal, and a big Vout to small Vout for the 10k hz signal.

White board work of the circuit. We got Vout to be 9.998 + .48i, which was close to the 1/2 signal out at omega = infinity.

In summary of class we learned about transform function and why we have and use it. Whenever we have a circuit that behaves differently with different omegas a transfer function is a very good way to find important information about it. We then some examples to find the zeros and poles of a signal source and then write code to plot it with a semilog function. We then did the last lab of the class of multiple signal sources and signal sweeps. We found that the higher the frequency the lower our Vout was is this circuit and that the output signal mimicked the input with its own signal ontop of the output signal. We also found that 1 khz sweep signal goes low Vout to high Vout for sweeps, and  for the 10 khz signal goes high Vout to low Vout for sweeps.