11/30/2021 4A_3_Amplifiers Gain.docx 1/8 Jim Stiles The Univ. of Kansas Dept. of EECS Amplifier Gain Q: So how do we specify gain in microwave amplifiers? A: First, for a given microwave amplifier, we connect a matched source (e.g., 0gZZ) to a matched load (e.g., 0LZZ). +−0Z0ZgV11/30/2021 4A_3_Amplifiers Gain.docx 2/8 Jim Stiles The Univ. of Kansas Dept. of EECS Gain is a ratio of power—a real value! We then determine/measure the available power of the source: 208gavlVPZ And also, the power delivered the load: 202LabsVPZ The gain G of a microwave amplifier is typically defined as the ratio of these two real values: absavlPGP11/30/2021 4A_3_Amplifiers Gain.docx 3/8 Jim Stiles The Univ. of Kansas Dept. of EECS Gain is frequency dependent More specifically, the gain of a microwave receiver is dependent on frequency: absavlωPGPωω Generally speaking, there will be a range of frequencies ω between Lω and Hω where the gain G ω will be (approximately) be equal to a constant midG (i.e., the mid-band gain). For frequencies outside this range, the gain will typically be small (i.e. midG ω G): mid L Hmid L HωωωG for ωωGG for ω or ω ω 11/30/2021 4A_3_Amplifiers Gain.docx 4/8 Jim Stiles The Univ. of Kansas Dept. of EECS If (say) G =15, then we know this is the gain within the amplifier bandwidth The width of this frequency range defines the amplifier bandwidth: f G f midG Lf Hf Amplifier Bandwidth11/30/2021 4A_3_Amplifiers Gain.docx 5/8 Jim Stiles The Univ. of Kansas Dept. of EECS Cascaded Amplifiers Now, consider the case where two matched amplifiers are cascaded: We ask ourselves the question: What is the total gain of the two combined (cascaded) amplifiers? absTavlPGP +− 0Z 0Z gVAG BG avlP absP ABavl absPP=11/30/2021 4A_3_Amplifiers Gain.docx 6/8 Jim Stiles The Univ. of Kansas Dept. of EECS What is the total gain? If the two amplifiers are matched, then the available power at the output of the first amplifier (AavlP) is equal to the power absorbed by the input of the second amplifier (BabsP). Thus: BAabsavlP GP and ABabsavlP GP And since ABavl absPP, we can determine: BAin ABB Babsdel avlP GP GP GGP +− 0Z 0Z gVAG BG avlP absP ABavl absPP=11/30/2021 4A_3_Amplifiers Gain.docx 7/8 Jim Stiles The Univ. of Kansas Dept. of EECS Total gain is the product of each individual gain! Therefore, we find that the total gain of the matched cascaded amplifiers is simply equal to the product of the individual gains! absABTavlPG GGP Moreover, if we were to cascade multiple amplifiers, then the gain of the total “chain”—from the input at the first amp to the output at the last amp—is (for N amplifiers): 1123...NnNnTGGG GGG11/30/2021 4A_3_Amplifiers Gain.docx 8/8 Jim Stiles The Univ. of Kansas Dept. of EECS Total gain in dB is the sum of each gain in dB Expressed with a decibel operator, we find the gain of cascaded amplifiers is: 1123...NNnnTdB dB dBGGG GGG And since log log logxyyx: 1312NnNnTdB dB dB dB dB dBGGGGGG
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