Camara Practice Problems 63-2

[lowcountrygamecock]

I am having trouble with control systems and have been really stumped with a question from the additional Camara Practice Problems book. Number 63-2. It's asking you to find the transfer function for a circuit diagram. I am with them down to where it's (3sV1+2sV3)/(5s+3)=(7V3/4). This step is where they equate the two V2 terms that had been solved for from the nodal equations. But where i get lost is how they go from that step to Vout/Vin=V3/V1 = (12S)/(27S+21). What am i missing there on that math? I don't understand that transition at all. Please help me!!!!!

 

[benbo]

I am having trouble with control systems and have been really stumped with a question from the additional Camara Practice Problems book. Number 63-2. It's asking you to find the transfer function for a circuit diagram. I am with them down to where it's (3sV1+2sV3)/(5s+3)=(7V3/4). This step is where they equate the two V2 terms that had been solved for from the nodal equations. But where i get lost is how they go from that step to Vout/Vin=V3/V1 = (12S)/(27S+21). What am i missing there on that math? I don't understand that transition at all. Please help me!!!!!

You may have already seen this. If I didn't go far enough back let me know.

Assuming you know how to get the

(3sV1+2sV3)/(5s+3)=(7V3/4).

Cross multiply

12sV1+8sV3 = 35sV3+21V3

Combine like terms

12sV1 = 27sV3+21V3

12sV1 = (27s+21)V3

V3/V1 = 12s/(27s+21) Divide top and bottom by three

V3/V1 = 4s/9s+7