Mathcad - ee217projtodonew2.mcd

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1 0 µwithR( S, R) µ ABCD2S S2ABCD( S, 50 ohm) . ohm , 1 50 ohm R µwithR Sparam N , I C , s , 1000 ohm = 1.248 µ Factor with Load Resistor 1.3 K and Mu Factor 1.2 1.1 1 100 1 .10 3 1 .10 4 Ballast Resistance (kohm) K Factor Mu Factor Desired K Factor Fig. 12: K and Mu vs. Ballast Resistor Rguess 0.1 kΩ Rneeded N , I C , s, Kval if K Sparam N, I C , s > Kval, 100 kΩ, root KwithR Sparam N, I C , s , Rguess Kval, Rguess Rneeded2 N , I C , s, Kval if µ Sparam N , I C , s > Kval, 100 kΩ, root µwithR Sparam N, I C , s , Rguess Kval, Rguess Rneeded2 N , I C , s, K val = 100 kΩ R L N, I C , s Rneeded N, I C , s, K val R L N, I C , s = 773.703 ohm It is interesting to plot the ballast resistor needed vs. the device size and current. These curves are shown in the following figures. From these plots we see the stability of the device increases with bias current and decreases with device size. Conversely we see we need a smaller parallel ballast resistor for more potentially unstable devices. Thus a smaller ballast resistor is needed for larger devices and devices with smaller currents. 1 .10 6 Ballast Resistor Need to make K=Kval Ballast Resistor Size (ohms) 1 .10 5 1 .10 4 1 .10 3 100 1 10 100 Number of Devices in Parallel Ballast Resistor Need to make mu=Kval Fig 13: Ballast Resistor vs. Device Size
2000 Ballast Resistor (ohms) 1500 1000 500 0 0 5 10 15 20 Resistance Needed w/ 25 Devices Resistance Needed w/ 50 Devices Resistance Needed w/ 75 Devices Bias Current (mA) Fig. 14: Ballast Resistor vs Current Simultaneous Conjugate Matching Analysis It is desirable from a gain perspective to simultaneously conjugate the input and output of the amplifier. This maximizes gain, but may not be optimal for noise as we shall see later. If the device is unilateral (i.e. the reverse isolation, S12, is zero) the conjugate matching impedances can be calculated directly from S11 and S22. In reality S12 is some non-zero value, so matching the input will change the impedance at the output. Simultaneous matching can be done iteratively, which can be tedious and time consuming. An easier method involves solving a second order equation for the desired values. The derivation of Zpopt is done in [4]. To use the equation the S-Parameters must first be recalculated with the necessary ballast resistor. KCL N, I C , s, Z S , Z L 1 1 1 Z S Z bias r b 1 r b 0 0 1 0 0 r b 1 j. ω . 1 C µ j. ω . 1 C µ r b Z π Z π j. ω . C µ g m j. ω . 1 1 1 1 C µ g m R L Z L r o r o 1 1 1 1 1 g m g m Z π r o Z e Z π r o KCLinv N, I C , s, Z S , Z L KCL N, I C , s, Z S , Z L 1
Page 1 and 2: 'HVLJQDQG$QDO\VLVRID *+]/RZ1RLVH$PS
Page 3 and 4: Introduction Low noise amplifiers a
Page 5 and 6: ∆f: The frequency spacing of the
Page 7 and 8: Architecture Selection Amplifier Ev
Page 9 and 10: Common Base Amplifier To find the d
Page 11 and 12: KCL N, I C , s, Z S , Z L 1 1 1 Z S
Page 13 and 14: 100 10 1 0.1 0.01 0.01 0.1 1 10 100
Page 15: Ballast Resistor Sizing The term ba
Page 19 and 20: Z popt SZ , 0 ∆ S . 11 , S 22 , S
Page 21 and 22: Solve r . b i . bn Z . e β β . V
Page 23 and 24: Noise Correlation Except in special
Page 25 and 26: n is the noise resistance represent
Page 27 and 28: Optimal Source Impedance to Trade-O
Page 29 and 30: Gain Analysis Z2Γ( Z) Z Z G T Γ G
Page 31 and 32: A 3 N, I C , Z S , s 1 , s 2 , s 3
Page 33 and 34: Optimizing Area and Current I C 0.0
Page 35 and 36: Impedance Matching High-pass impeda
Page 37 and 38: Low Frequency Stabilization It is d
Page 39 and 40: To insure stability over the spectr
Page 41: It is possible to use on-chip induc
Page 49: ... . 1 s 1 s 2 s . 3 C je N, I . C

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