Stability

# Stability - Sheet 1 of 9 Stability Considerations When embarking on any amplifier design it is very important to spend time checking on the

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Sheet 1 of 9 Stability Considerations When embarking on any amplifier design it is very important to spend time checking on the stability of the device chosen, otherwise the amplifier may well turn into an oscillator. The main way of determining the stability of a device is to calculate the Rollett’s stability factor (K), which is calculated using a set of S-parameters for the device at the frequency of operation. The calculations are long winded and it is much quicker to simulate under ADS. The conditions of stability at a given frequency are | Γ in | < 1 and | Γ out | < 1,and must hold for all possible values Γ L & Γ S obtained using passive matching circuits. We can | to give us an indication to whether a device is likely to oscillate or not or whether it is conditionally/unconditionally stable. 1 S . S S . S where , 1 S . S 2 S S - 1 K 21 12 22 11 21 12 2 2 22 2 11 < = > + = The parameters must satisfy K > 1 and | | < 1 for a transistor to be unconditionally stable. Once we have calculated the K factor and find the device to be unconditionally stable we can calculate the Maximum available gain (MAG):- ( ) 1 K - K S S G 2 12 21 MAX = Where K is on the limit of unity the above equation reduces down to:- 12 21 MAX S S G = In this case the MAG is known as the maximum stable gain MSG. In the case of the design we need to calculate the stability factor at 4 & 6GHz, however it is important to check the stability factor from low frequencies up to the f T of the device as instabilities may occur at other frequencies even though the device is stable within the pass- band. () ( ) () ( ) 0.26615 and 0.5159 2 . 131 - 0.5159 33957 . 0 38845 . 0 tan 33957 . 0 0.38845 - polar to convert j0.33957 - 0.38845 - j0.1266 - 0.15094 - j0.46617 - 0.23751 - n subtractio for cartesian to convert 130 0.19707 - 153 - 0.5232 97) 33x2.986 (0.066 - 61) - 92x0.607 - 0.862 ( S . S S . S 4GHz at K of Evaluation 2 1 2 2 21 12 22 11 = = = + = = = = =

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Sheet 2 of 9 () () () 0.39 0.394 0.1551 ) 130 197 . 0 ( 2 0.26617 0.368 - 0.743 - 1 97 986 . 2 33 066 . 0 2 26617 . 0 607 . 0 0.862 - 1 S . S 2 S S - 1 K 2 2 21 12 2 2 22 2 11 = = + = + = + = x Therefore, at 4GHz the transistor is conditionally stable as K < 1 and therefore, we will have to be careful in the way the transistor is matched. Similarly the K factor at 6GHz was calculated to be 0.585 and | | = 0.42. Now that it is known that the transistor is conditionally stable it is now necessary to calculate and plot the corresponding stability circles on a Smith chart so that the no-go areas for matches can be highlighted.
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## This note was uploaded on 01/07/2011 for the course ECE 166 taught by Professor Staff during the Spring '08 term at UCSD.

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Stability - Sheet 1 of 9 Stability Considerations When embarking on any amplifier design it is very important to spend time checking on the

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