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Design of an amplifier with emitter degeneration

I’m trying to solve a question that says to find \$gm\$ and \$R_c\$, considering a gain of 50 using a BC547b transistor. But I can’t find a way to calculate these parameters with the information I have. Could someone help me?

The BC547 model:

*PVDB
*DATABOOK PHILIPS
.MODEL BC547B NPN (BF=530 NE=1.3 ISE=9.72F IKF=80M IS=20F VAF=50V

  • BR=10 NC=2 ISC=47P IKR=12M VAR=10
  • RB=280 RE=1 RC=40 TR=.3U
  • CJE=12P VJE=.48 MJE=0.5 CJC=6P VJC=.7 MJC=.33 TF=.5N)

So, because of that I’m considering Va = 50V, Is = 20e-15 and Beta = 530. Right?

The circuit of this question:

Circuit

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