Upper 3 dB frequency

C.I. Using Goal Functions to Find the Upper 3 dB Frequency... 

A second method can be used to find the upper 3 dB frequency found in the previous section. We will continue from the end of the previous section. First, hide the cursors by selecting Trace, Cursor, and then Display from the Probe menus. Next, select Window and then New Window to open a new Probe window ... 

The right window pane lists the available goal functions. Use this list to locate the Upper3dB goal function. We would like to find the upper 3 dB frequency of the voltage trace V(VO), so enter the following Trace Expression, upper3dB(V(VO)) ... 

We can see that the mid-band gain is 45.7 dB, the upper 3 dB frequency is 6.4 MHz, and the lower 3 dB frequency is 64.4 Hz. You can also use the Upper3dB and Lower3dB goal functions to find upper and lower -3dB frequencies. Select Trace and then Eval Goal Function to evaluate these functions ... 

EXERCISE 5-B For the inverting op-amp below, find the upper 3 dB frequency for mid-band gains of -1, -10, -100, and -1000. Show the Bode magnitude plots for all of the gains on the same graph. 

Suppose that for the example of Section 5.F, we would like to see a plot of how the upper 3 dB frequency is affected by the value of the feedback resistor, Rf. This plot can be accomplished using the Performance Analysis capabilities of Probe. Repeat the procedure of Section 5.F. When you obtain the plot on page 310, you may continue with this section. The plot on page 310 is repeated as follows ... 

We now wish to plot the upper 3 dB frequency versus RFj/al. Select Trace and then Add Trace... 

When plotted on a log-log scale, we can easily see the relationship between the value of Rf and the upper 3 dB frequency. 

From this plot, we see that as RF increases the upper -3 dB frequency goes down, or as the gain increases the upper -3 dB frequency goes down. Another way to state this is that the upper -3 dB frequency times the circuit gain is approximately constant. We shall show this in the next exercise. 

The function Max(V(Vo)) gives us the maximum value of Vo for each trace. Since the input was one volt, the Max(V(Vo)) is also the maximum gain for each trace. Thus Max(V(Vo)) upper3dB(V(Vo)) is the maximum gain for each trace times the upper 3 dB frequency for each trace, or the gain times bandwidth for each trace. For this circuit, the maximum gain occurs at midband frequencies. 

When we design a circuit with tolerance, we may sometimes want to find the worst case upper or lower 3 dB frequency with component tolerances. Unfortunately, calculating a 3 dB frequency requires that we find the mid-band gain and then find the frequency where the gain is 3 dB less than the mid-band. This type of calculation cannot be specified in the Monte Carlo/Worst Case dialog box. However, we can run a Monte Carlo analysis and then determine the 3 dB frequency using the Performance Analysis capabilities available in Probe. In this example, we will illustrate finding the maximum lower 3 dB frequency (FL), minimum upper 3 dB frequency (FH), and maximum and minimum bandwidth (FH - FL) for a common-emitter amplifier. Wire the circuit below ... 

This function finds the lower 3 dB frequency and marks the coordinates of the point xl and yl. It then finds the upper 3 dB frequency and marks the coordinates of the point x2 and y2. The function returns the bandwidth, x2 - x1. 

We see that the maximum lower 3 dB frequency is at 80.2421 Hz. In the screen capture above, the number of histogram divisions has been set to 100. See page 519 for instructions on how to change this setting. To view the upper 3 dB frequencies, add the trace upper3dB(V(VO)) ... 

The maximum frequency of the electro-optic effect in Hthium niobate is probably in the hundreds of gigahertz. Thus, in practice the upper limit on the frequency response is set by electrical considerations. The key parameter that divides modulators into one of two types is the ratio of the modulation period of the maximum modulation frequency to the optical trmsit time past the electrodes. If the optical transit time is short relative to the period of the maximum modulation frequency, then the modulator signal will essentially be constant during the optical transit time. In this case the electrodes can be treated as lumped elements, see Fig. 9.54(c), which means that the upper 3-dB frequency is simply determined by the RC rolloff due to the electrode capacitance and resistance as shown in Fig. 9.57. Atypical frequency response of a low-frequency MZM is shown in Fig. 9.59(a). 

Run the PSpice simulation Select PSpice and then Run from the Capture menu bar. When the simulation is complete, the Probe window will open. Add the trace DB(V(VO) ) to plot the gain in decibels. Use the cursors to label the mid-band gain, and upper and lower -3 dB frequencies. Your cursor values may be slightly different than those shown here. 

The name of the function is upper3dB. It has 1 input argument. 1 sfle means search the first input forward and find a level. The level we are looking for is 3 dB less than the maximum (max-3). The n means find the specified level when the trace has a negative-going slope. When the point is found, the text 1 designates its coordinates as xl and yl. The function returns the x-coordinate of the point (upper3dB(1) = x1). The x-axis of a frequency trace is frequency, so this function returns the frequency of the upper 3 dB point. A second function is ... 

Bandwidth The range of frequencies over which a system instantaneously operates, i.e., passes a signal, usually taken as the difference between the upper —3 dB point in the response and the lower —3 dB... 

Amplifier bandwidth. The range of signal frequencies over which an amplifier is capable of undistorted or unattenuated transmission. An operational amplifier should transmit DC voltage accurately the upper (bandwidth) limit is defined as the 3-dB point (attenuation factor of two). Because bandwidth can vary with gain, the product of gain x bandwidth can be a more useful parameter. 

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