![]() ![]() The total impedance: Z(s) = R + sL = R (1 + sL/R) Click/tap the circuit above to analyze on-line or click this link to Save under Windows You can use TINA Analysis to get the equation of the equivalent impedance by choosing Analysis – Symbolic analysis – AC Transfer. Second order polynomials with complex conjugate roots lead to a more complicated Bode plot that will not be considered here.įind the equivalent impedance and sketch it. ![]() Between these frequencies, the phase diagram can be approximated by a straight line which connects the points (0.1* w 1 0) and (10* w 1 – 90 ° ).Ī constant multiplier factor in the function is plotted as a horizontal line parallel to w -axis. The phase is 0 at small frequencies, -90 ° at high frequencies, and -45 ° at w 1 = 1/T. The last first order term, 1/(1+sT), has a –20 dB/decade slope starting at the angular frequency w 1 =1/T. Between these frequencies, the phase diagram can be approximated by a straight-line segment which connects the points (0.1* w 1 0) and (10* w 1 90 ° ). A good approximation for phase is that it is zero until 0.1* w 1 = 0.1/T and is nearly 90 ° above 10* w 1 = 10/T. The phase equals zero at small frequencies, 90 ° at high frequencies and 45 ° at w 1 = 1/T. The amplitude plot is a horizontal line until w 1 = 1/T, after which it slopes upward at 20 dB/decade. The next first order term to sketch is 1+sT. Similarly, the absolute value of the term K/ s has a -20 dB/decade slope the phase is -90 ° at any frequency but it crosses the w axis at w = K, where the absolute value of the fraction The next first order term (in the second example), s -1 = 1/s, is similar: its absolute value has a -20 dB/decade slope its phase is -90 ° at any frequency and it crosses the w -axis at w = 1. The curve of K* s also has a 20 dB/decade slope but it crosses the axis at w = 1/K i.e., where the absolute value of the product ½ K* s ½ = 1. The phase of this term is 90 ° at any frequency. The curve of the absolute value of a first order term s has a 20 dB/decade slope crossing the horizontal axis at w = 1. Remembering that the product of terms in the transfer function will be seen as the sum of terms in the logarithmic domain, we will see how to sketch the individual terms separately and then add them graphically to obtain the final result. Because the vertical axis is represented in dB, it is a logarithmic scale. Now we will see how transfer functions like the ones above can be quickly sketched (transfer function gain in dB versus frequency in Hz). The –3 dB point implies that A is 1/1.41 = 0.7.Ī typical transfer function looks like this: Converting from A in dB to A in volts/volt, we solve 3 dB = 20 log10 A and obtain log10 A = 3/20 and hence. The 3 dB point on a Bode plot is special, representing the frequency at which the amplitude has increased from a constant value by 3 dB. Here’s a summary of the important principles of Bode plots, and the rules for sketching them. For simpler expressions, we substitute s for frequency: j w = s.īecause the quantities being plotted are plotted on a logarithmic scale, the curves belonging to the different terms of the product can be added. The poles are sometimes called the cutoff frequencies of the network. The end points of these straight-line segments projected onto the frequency axis fall on the pole and zero frequencies. Idealized Bode plots are simplified plots made up of straight-line segments. ![]() The roots of the numerator are the zeros of the function while the roots of the denominator are the poles. The first step is to find the roots of the polynomials. The function to be sketched is generally a fraction or a ratio with a numerator polynomial and a denominator polynomial. In the paragraphs that follow, we will present these rules and compare sketched straight-line approximation curves with TINA’s exact curves. Nevertheless, understanding the rules for drawing Bode plots will enhance your mastery of circuits. TINA has very advanced facilities for Bode plots. Today, few engineers draw Bode plots by hand, relying instead on computers. The horizontal scale for frequency is logarithmic. ![]() The amplitude A is presented as 20log10(A). The dependence of a complex quantity upon frequency can be represented on a complex plane (Nyquist diagram) or on real planes as separate plots of the absolute value (amplitude plot) and the phase (phase plot).īode plots use a linear vertical scale for the amplitude plot, but since dB units are used, the effect is that the vertical scale is plotted according to the logarithm of the amplitude. Most of the interesting functions of AC circuits –complex impedance, voltage transfer function, and current transfer ratio– depend on frequency. ![]()
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Lightroom and Photoshop are both powerful digital photography post-processing (photo editing) programs that share a lot of features and tools but differ in the way these are used or applied. ![]() Thank you.Let me know in the comment, whether I did a good job or if you’d like to hear more about it. Thanks for reading and do leave your kind comments. You can check the gimp VS photoshop comparison to that end. But if you don’t want a paid software, gimp can always be downloaded free. For an artist or illustrator though, Photoshop is a need. After all there is always a need to get those odd edits that require one software or the other. Those being some of the points to consider, most photographers will find wanting the need for both software. Any major image corrections like completely removing something from a photo, replacing with the background, etc.Ħ. 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