# Transresistance Amplifier

#### tquiva

Joined Oct 19, 2010
176

Problem
You are designing a transresistance amplifier for a cell phone. This amplifier will take a voltage from the RF transmitter and supply it to the cell phone antenna. You are given the following design specifications:

 The output resistance of the RF circuitry is 50 Ω (source resistance)
 The RF circuitry outputs a signal of up to 5 Vrms
 The amplifier provides a signal to the antenna, which can be modeled as a 50-Ω resistor
 The amplifier provides the antenna with a voltage of at least 10 Vrms without saturating
 The cell phone is multi-band, so it transmits at a frequencies ranging from 900 MHz to 1.1 GHz

a) What is a desirable amplifier bandwidth? Sketch a bode plot of the amplifier's transfer function. Label the 3-dB bandwidth and break points.
b) Draw a schematic of the amplifier circuit, including the RF circuitry input and the antenna load. Use one of the four amplifier circuit models - voltage amplifier, current amplifier, transconductance amplifier, or transresistance amplifier. Simplify the circuit as much as possible. You can assume the ideal value for the internal amplifier resistance (Ri and Ro).
c) What is the minimum Rm that will meet the design specifications? Is it desirable to design the amplifier to the minimum gain requirement? Why or why not?
d) Assume the minimum value of Rm is 100 V/A. What is the peak voltage supplied to the antenna? What are the values of Av , Ai, and Ap?
e) What is the minimum dc power needed by the amplifier? Assume the amplifier is 90% efficient.

So to begin this problem, I first drew a simple diagram of what is going on, and I drew a transresistance amplifier based on the specs. I then tried solving for the input resistance and output resistance. The final circuit of the transresistance model is at the bottom of the page. Image is in the first attachment below.

I made the voltage source to the amplifier 5 Vrms since this is the output of the RF circuit, and since the source resistance is 50 Ω, I found i_i to be 0.14 A.
Next, should I label the resistor near the output as 50 Ω? I'm not too sure on this since the spec says "The amplifier provides a signal to the antenna, which can be modeled as a 50-Ω resistor." But I went ahead and tried this, and have Ro to be 50 Ω.

I also know that Rm=Vo/i1. So in this case, i1=Vs/Rs=5V/50Ω=0.1A. Then Rm=Vo/i1=10V/1A=10 V/A
Is this correct?

For part a) when it asks for the desirable bandwidth, I have:
(1.1e9 Hz) - (900e6 Hz) = 2e8 Hz
If I plot this onto a bode plot of |T| (db) vs. f (Hz), would the constant value of |T| be 20log(2) since Vo/Vi = 10V/5V = 2V ? The bode plot is the second attached image.

I then proceeded to part (b) with a voltage amplifier model, then to parts (c) and (d). I am quite unsure of how to find the min. DC power in part (d). I am very hesitant about my work so far, but if someone has the time, will you please go over it and give me some feedback?

I'm not sure how else to proceed with this problem in giving it the right values and parameters. I apologize for my ignorance here.... I tried googling this and rereading my book, but am still confused. Any help here is greatly appreciated.

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