# Amplifier gain at a given frequency the maximum gain

• Notes
• 44

This preview shows page 27 - 32 out of 44 pages.

Amplifier Gain At a given frequency, the maximum gain that an amplifier can deliver is limited by either its G max = G T ,max or by stability G MSG AMPLIFIER GAIN Unconditionally Stable: G T ,max Potentially Unstable: MSG Stabilize transistor unilateral bilateral G P circles G T circles unilateral bilateral G P circles G T circles
ECE145A/ECE218A A MPLIFIER D ESIGN 12/14/07 28 Prof. Stephen Long, ECE/UCSB Constant Gain Circles: Unilateral Case Now that we have determined a method to find the stable regions of Γ S and Γ L and if necessary to add resistance to guarantee stability, we can explore other considerations for setting the gain. 1. Avoid instability – then 2. Choose Γ S , Γ L for simple MN manipulation 3. Q selection in narrowband design 4. Max. unilateral gain or Max. stable gain. Unilateral: S 12 =0 This is never really true, but it can be a useful approximation in some cases. Why? if S 12 =0, then Γ in = S 11 and Γ out = S 22 no interaction between input and output. Can we really consider device to be unilateral? S 12 0 ever But we can estimate maximum gain error: 1 1 + u ( ) 2 < G T G TU < 1 1 u ( ) 2 u = S 12 S 21 S 11 S 22 1 S 11 2 ( ) 1 S 22 2 ( ) unilateral figure of merit. if this is small (it might be at low enough frequency) the unilateral approximation is justified. Can a unilateral device still be unstable? Yes. It is possible that |S 11 | > 1 and/or |S 22 | > 1.
ECE145A/ECE218A A MPLIFIER D ESIGN Unilateral Transducer Power Gain G TU = 1 − Γ S 2 1 S 11 Γ S 2 ± ² ³ ´ ³ S 21 2 1 − Γ L 2 1 S 22 Γ L 2 ± ² ³ ´ ³ = G S G 0 G L fraction of gain/loss due to input match fraction of gain/loss due to output match If unilateral, G T = G TU = unilateral transducer power gain How do we obtain the maximum G TU (sometimes called maximum available gain )? . 0 TU G s G 0 G L S 11 S 22 Γ L Z 0 Z 0 Input Match Transistor Output Match Γ S
12/14/07 29 Prof. Stephen Long, ECE/UCSB
ECE145A/ECE218A A MPLIFIER D ESIGN 12/14/07 30 Prof. Stephen Long, ECE/UCSB Now describe Gain circles . (when unilateral assumption is valid) We wish to describe the variation in G T with Γ S and Γ L in a graphical form. Let’s assume that S 11 < 1 and S 22 < 1 . * Values of Γ S and Γ L that produce constant gain lie on circles in the Γ plane. * Maximum gain occurs when Γ S = S 11 * and Γ L = S 22 * . These are points on Γ S and Γ L planes respectively. The centers of the circles lie on the line connecting these points with the origin. * By necessity, 0 dB circle will always pass through origin Γ S = 0 or Γ L = 0 ( ) . This comes about because G S =1 and G L = 1 when Γ S = Γ L = 0, ie. matched to Z 0 . Circles of constant G L can be similarly drawn on the Γ L plane. In ADS, input and output gain vs Γ S or Γ L can be plotted using Gscir or GLcir functions. S 11 * X r gs C gs Γ S plane ∠ = ∠ S 11 * gain = G S , max circles of constant G S
ECE145A/ECE218A A MPLIFIER D ESIGN 12/14/07 31 Prof. Stephen Long, ECE/UCSB
• • • 