# Prelab 6

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## 1) Doppler ultrasound system receiver

In a previous lab, we built the doppler ultrasound transmit amplifier. We recall that this amplifier takes the 3.3 Vpp 40 kHz square wave (which will eventually be created by the Teensy) and amplifies it to a ~26-29 Vpp square wave that is then sent to the ultrasound transmitter.

The ultrasound waves then bounce off a (maybe moving) object, and are turned back into a voltage by the ultrasound receiver. When we probed the receiver in lab 4, it was a tiny signal. We'll need to amplify it before processing it further. That's the goal of the receiver amplifier in lab 6.

## 2) Doppler Ultrasound Gain Stage

In this prelab, we'll design the receiver amplifier. Below is a simplified schematic of the receive stage:

Modeling the speaker as a voltage source of value v_{IN}, determine an expression for v_{OUT} as a function of v_{IN}, R4, and R5.

Enter v_{IN} as vIN, R4 as R4, R5 as R5.

v_{OUT} [V] =

Now we need to pick values for R4 and R5. Choose R4 and R5 such that:

• The magnitude of the overall gain is between 9 and 11. Remember that the gain does not include any voltage offset in the output relationship. This gain should be enough to amplify the signal, though we'll ensure this in lab.

• The resistor values should be in the 10 k\Omega - 200 k\Omega range. Why? Because if you look at the ultrasound transducer datasheet you'll see that the receiver's output impedance (similar to the output resistance...don't worry we'll cover what impedance means soon) is around 2 k\Omega at 40 kHz. This means that the ultrasonic receiver can be modeled as a Thevenin equivalent circuit with a 2 k\Omega Thevenin resistance (shown below). The transducer's Thevenin voltage along with its Thevenin resistance forms a voltage divider with R4, the output of which is actually the signal sent into the amplifier, and so we want R4 \gg 2 k\Omega. So 10 k\Omega is a reasonable lower limit. If the resistor values are too high, they tend to introduce noise and exacerbate offsets and other non-idealities of the op-amp.

• Resistor values should be part of the standard 5% resistor values.

Enter your values as a Python list in the following order: [R4, R5]. Thus, if you chose R4 = 10k, R5 = 20k, you would enter [1e4, 2e4].

Enter your circuit parameters here [R4, R5]:

## 3) Next up

That's it for now.