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Problem 24-1 Suppose a circuit has an rms ac input of 100 V and an rms ac output of 140 V What is the gain in decibels First, find the ratio Eout/Ein Because Eout = 140 V rms and Ein = 100 V rms, the ratio is 140/100, or 140 Next, find the logarithm of 140 This is about 1146128036 Finally, multiply this number by 20, getting something like 2292256071 Round this off to three significant figures, because that s all you re entitled to, getting 229 dB Problem 24-2 Suppose a circuit has an rms ac input voltage of 242 V and an rms ac output voltage of 199 V What is the gain in decibels Find the ratio Eout/Ein = 199/242 = 0822 (The three dots indicate extra digits introduced by the calculator You can leave them in until the final roundoff) Find the logarithm of this: log 0822 = 00849 The gain is 20 times this, or 1699 dB, which rounds off to 170 dB For Current Current gain or loss is calculated in the same way as voltage gain or loss If Iin is the rms ac input current and Iout is the rms ac output current specified in the same units as Iin, then:

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Gain (dB) = 20 log(Iout /Iin )

If there is a partial search term in the text field, we can send it to Google Suggest to get its suggestions; here s how you check if there is a partial search term already entered:

For Power The power gain of a circuit, in decibels, is calculated according to a slightly different formula If Pin is the input signal power and Pout is the output signal power expressed in the same units as Pin, then:

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If there is a search term waiting, we can send it to Google Suggest We ll do that via a PHP script, googlephp, using the GET method, which means we have to URL-encode our data We ll send the partial search term to googlephp (which will forward that term on to Google Suggest) using the argument name qu (short for query) Here s how we send the partial search term to googlephp, by calling a function we ve named getData:

Gain (dB) = 10 log (Pout /Pin ) The coefficient (that is, the factor by which the logarithm is to be multiplied) in the formula for power gain is 10, whereas for voltage and current gain it is 20

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Problem 24-3 Suppose a power amplifier has an input of 503 W and an output of 125 W What is the gain in decibels

Why do we communicate with Google Suggest via a PHP script Why can t we just contact Google Suggest directly, from this web page These are important questions The answer is that this is an issue of security If a web browser sees that your Ajax script is trying to contact a server that s not the same server on which your web page resides, it will get suspicious That s the case here the server on which Google Suggest resides is not the same as our server In cases like this, the browser puts up an (annoying) dialog box, asking the user if it should proceed That kind of thing destroys the utility of Ajax, which is supposed to operate seamlessly, behind the scenes To get around this problem, you can use server-side programming, on your own server, to connect to the foreign server That s what we re doing here we re connecting to Google Suggest via googlephp to avoid security issues (and we ll write googlephp a bit later) Okay, we re nearly done with the askGoogleSuggest function The last step is to clear the drop-down list box if the user has erased the text in the search text field, which we do like this:

Find the ratio Pout/Pin = 125/503 = 2485 Then find the logarithm: log 2485 = 1395 Finally, multiply by 10 and round off The gain is thus 10 1395 = 140 dB

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The getData function in this example just takes a URL argument, named dataSource:

Problem 24-4 Suppose an attenuator (a circuit designed deliberately to produce power loss) provides 10 dB power reduction The input power is 94 W What is the output power An attenuation of 10 dB represents a gain of 10 dB We know that Pin = 94 W, so the unknown in the power gain formula is Pout We must solve for Pout in this formula: