Note: This part of the lab is just to develop your intuition about -amplifiers and biasing, and to have fun with music! There are no responses -that need to be checked.
-The graph plots the selected voltages from the amplifier circuit below. You -can also listen to various signals by selecting from the radio buttons to -the right of the graph. This way you can both see and hear various signals. -You can use the sliders to the right of the amplifier circuit to control -various parameters of the MOSFET and the amplifier. The parameter \(V_{MAX}\) -sets the maximum range on the plots. You can also select an input voltage -type (e.g., sine wave, square wave, various types of music) using the drop -down menu to the right of the graph. When describing AC signals, the -voltages on the sliders refer to peak-to-peak values.
-1. To begin your first experiment, go ahead and use the pull down menu to -select a sine wave input. Then, adjust the sliders to an approximate -baseline setting shown below.
-Baseline setting of sliders:
-
-\(V_{S}=1.6V\), \(v_{IN}=3V\), \(Frequency=1000Hz\), \(V_{BIAS}=2.5V\), \(R=10K\Omega\), \(k=1mA/V^{2}\), \(V_{T}=1V\), \(V_{MAX}=2V\).
You will observe in the plot that the baseline setting of the sliders for -the various amplifiers parameters produces a distorted sine wave signal for -\(v_{OUT}\). Next, go ahead and select one of the music signals as the input and -listen to each of \(v_{IN}\) and \(v_{OUT}\), and confirm for yourself that the -output sounds distorted for the chosen slider settings. You will notice -that the graph now plots the music signal waveforms. Think about all the -reasons why the amplifier is producing a distorted output.
-2. For the second experiment, we will study the amplifier's small signal -behavior. Select a sine wave as the input signal. To study the small -signal behavior, reduce the value of \(v_{IN}\) to 0.1V (peak-to-peak) by -using the \(v_{IN}\) slider. Keeping the rest of the parameters at their -baseline settings, derive an appropriate value of \(V_{BIAS}\) that will ensure -saturation region operation for the MOSFET for the 0.1V peak-to-peak swing -for \(v_{IN}\). Make sure to think about both positive and negative excursions -of the signals.
-Next, use the \(V_{BIAS}\) slider to choose your computed value for \(V_{BIAS}\) and -see if the observed plot of \(v_{OUT}\) is more or less distortion free. If -your calculation was right, then the output will indeed be distortion free. -Next, select one of the music signals as the input and listen to each of -\(v_{IN}\) and \(v_{OUT}\), and confirm for yourself that the output sounds much -better than in Step 1. Also, based on sound volume, confirm that \(v_{OUT}\) is -an amplified version of \(v_{IN}\).
-3. Now go ahead and experiment with various other settings while listening -to the music signal at \(v_{OUT}\). Observe the plots and listen to \(v_{OUT}\) as -you change, for example, the bias voltage \(V_{BIAS}\). You will notice that -the amplifier distorts the input signal when \(V_{BIAS}\) becomes too small, or -when it becomes too large. You can also experiment with various values of -\(v_{IN}\), \(R_{L}\), etc., and see how they affect the amplification and distortion.
-Graph:
-Listen to:
-Note: Use this part of the lab to build your intuition about filters and frequency response, and to have fun with music! There are no responses that need to be checked.
-Recall from the audio lab in Week 5 that the graph plots the selected voltages from the circuit shown below. This week the circuit is an RC filter. You can also listen to various signals by selecting from the radio buttons to the right of the graph. This way you can both see and hear various signals. You can use the sliders to the right of the circuit to control various circuit and input signal parameters. (Note that you can get finer control of some of the slider values by clicking on the slider and using the arrow keys). Recall that the parameter \(V_{MAX}\) sets the maximum range on the graph. You can also select an input voltage type (e.g., sine wave, square wave, various types of music) using the drop down menu to the right of the graph. When describing AC signals, the voltages on the sliders refer to peak-to-peak values.
-1. To begin your first experiment, use the pull down menu to select a sine wave input. Then, adjust the sliders to these approximate baseline settings:
-
-\(v_{IN} = 3V\), \(Frequency = 1000 Hz\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
-
-Observe the waveforms for \(v_{IN}\) and \(v_C\) in the graph. You can also listen to \(v_{IN}\) and \(v_C\). You will observe that the amplitude of \(v_C\) is slightly smaller than the amplitude of \(v_{IN}\).
-
-Compute the break frequency of the filter circuit for the given circuit parameters. (Note that the break frequency is also called the cutoff frequency or the corner frequency).
-
-Change the frequency of the sinusoid so that it is approximately 3 times the break frequency.
-
-Observe the waveforms for \(v_{IN}\) and \(v_C\) in the graph. Also listen to \(v_{IN}\) and \(v_C\). Think about why the sinusoid at \(v_C\) is significantly more attenuated than the original 1KHz sinusoid.
-
-Keeping the input signal unchanged, observe the waveforms for \(v_{IN}\) and \(v_R\) in the graph. Also listen to \(v_{IN}\) and \(v_R\). Think about why the sinusoid at \(v_R\) is significantly louder than the sinusoid at \(v_C\).
2. Next, use the pull down menu to select a music signal of your choice. Adjust the sliders to the approximate baseline settings:
-
-\(v_{IN} = 3V\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
-
-Listen to the signals at \(v_{IN}\) and \(v_C\). Notice any difference between the signals?
-
-Next, increase the capacitance value and observe the difference in the sound of \(v_{IN}\) and \(v_C\) as the capacitance increases. You should notice that the higher frequency components of \(v_C\) are attenuated as the capacitance is increased.
-Convince yourself that when the signal is taken at \(v_C\), the circuit behaves like a low-pass filter.
3. Re-adjust the sliders to the approximate baseline settings:
-
-\(v_{IN} = 3V\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
-
-Try to create a high-pass filter from the same circuit by taking the signal output across a different element and possibly changing some of the element values.
-
Graph:
-Listen to:
-\(I(s) = \frac{1}{R + Ls + 1/Cs}V_{in}(s) = \frac{s/L}{s^2 + sR/L + 1/LC}V_{in}(s)\)
-\(I(s) = \frac{s/L}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s)\)
-\(\omega_0 = \frac{1}{\sqrt{LC}} , \alpha = \frac{R}{2L}\)
-Band-Pass Filter:
-\(V_r(s) = RI(s) = \frac{sR/L}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{2\alpha s}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{2\alpha s}{(s-s_1)(s-s_2)}V_{in}(s)\)
-Gain magnitude: \(G_R = \frac{2\alpha w}{|j\omega - s_1||j\omega - s_2|}\)
-Phase: \(\Phi_R = \pi/2-\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)
-Low-Pass Filter:
-\(V_c(s) = I(s)/sC = \frac{1/LC}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{\omega_0^2}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{\omega_0^2}{(s-s_1)(s-s_2)}V_{in}(s)\)
-Gain magnitude: \(G_C = \frac{\omega_0^2}{|j\omega - s_1||j\omega - s_2|}\)
-Phase: \(\Phi_C = -\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)
-High-Pass Filter:
-\(V_l(s) = sLI(s) = \frac{s^2}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{s^2}{(s-s_1)(s-s_2)}V_{in}(s)\)
-Gain magnitude: \(G_L = \frac{\omega^2}{|j\omega - s_1||j\omega - s_2|}\)
-Phase: \(\Phi_L = -\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)
-Under-Damped: \(\alpha < \omega_0\)
-Complex roots: \(s_{1,2} = -\alpha \pm j\sqrt{\omega_0^2 - \alpha^2}\)
-Critically-Damped: \(\alpha = \omega_0\)
-Double real root: \(s_{1,2} = -\alpha\)
-Over-Damped: \(\alpha > \omega_0\)
-Real roots: \(s_{1,2} = -\alpha \pm\sqrt{\alpha^2 - \omega_0^2}\)
-Graph:
-Listen to:
-