## ECEN 1400 - Introduction to Digital and Analog Electronics

#### Goals of this Lab

• Analyze and measure a radio frequency (RF) amplifier for AM radio.
• Learn about inductors and resonant circuits.
• Wind and measure an inductor on a ferrite rod (loopstick antenna for AM radio).
• Learn about side effects of building RF circuits on a breadboard.
• Test the completed AM radio.

#### Prelab

Here is a link to a short video of the completed radio in action.

P1. Radio Frequency (RF) Amplifier. The primary function of the RF amplifier in a radio receiver is to amplify the small voltage (on the order of a few tens of microvolts) of the signal picked up by the antenna for further processing, e.g., by the demodulator. A secondary, related function is to provide a high enough input impedance so that the received signal can be filtered using resonant circuits.

The DC-biasing portion of a 2-transistor RF amplifier is shown in the schematic below.

Use the current-controlled current source model for the transistors to determine the base and emitter voltages of the first transistor and the collector voltage and collector current of the second transistor. Assume a beta of approximately 200 for the transistors. Then simulate the circuit in Multisim and measure the same quantities. Compare the results and comment on differences.

Next, add the components shown in the following schematic to complete the AC portion of the RF amplifier.

Measure the gain of the circuit at 100 kHz, 300 kHz, 500 kHz, and 1 MHz. Note that the source (AC Voltage under Signal Voltage Sources in Multisim) is set to 100 uVpk (peak amplitude, not peak-to-peak) and take this into account in your gain computation if you use the Vpp reading from the oscilloscope.

To measure the input resistance of the RF amplifier at f=100 kHz, use the schematic below and vary resistor R5 until the output voltage drops to one half of the level obtained without R5. Compare the resulting input resistance with the one you measured in the last lab at the input of the AM demodulator circuit.

The next schematic shows the RF amplifier with an input attenuator so that a small enough input voltage can be created, e.g., using the waveform generator in Multisim or in the lab.

Compute the attenuation factor of the input attenuator and verify your computation using a simulation in Multisim.

P2. Inductors and How to Measure an Inductor. An inductor is a passive device that can store energy in its magnetic field. Two examples of inductors (solenoid on the left, toroid on the right) are shown in the figure below.

The i-v relationship for an inductor is:

Compare this to the i-v relationship for a capacitor:

We say that inductors and capacitors are duals of each other since the roles of voltage and current are exchanged between them.

Inductance L is measured in henry (H). Typically, L of an inductor made from a wire-wound coil is proportional to the number of turns N squared. For a solenoidal inductor wound (in a single layer) on a core with permeability u, L can be computed as:

Using sinusoidal voltages and currents and phasors, the impedance (complex-valued resistance) ZL of an inductor is obtained as follows.

Combining resistors, capacitors, and inductors results in interesting circuits that exhibit resonant behavior, similar to the behavior of strings in musical instruments. Resonant circuits are widely used as filters in radio transmitters and receivers and in other signal processing applications. The figure below shows a series combination of R, L, and C. Note that in practice all inductors have some amount of resistance. Thus, R in the figure can either be thought of as a separate element or as being part of a (real) inductor.

The interesting result for the equivalent impedance Zeq is that it is minimal in magnitude and equal to R at the resonant frequency f0 = 1/(2*pi*sqrt(L*C)). Thus, if f0 and C are known, then an unknown inductor can be characterized in terms of L and R (resistance of inductor) at frequency f0. Note that for practical inductors L and R are generally frequency dependent. The inductor resistance R includes the wire resistance and losses in the core around which the inductor is wound.

To measure an inductor, the following setup can be used.

Assume that the values of R1 (the 50 ohm series resistance of a real waveform generator) and C1 are known. To determine the resistance R2 and the inductance L1 of the inductor, proceed as follows.

• Set the waveform generator to generate a sinewave with a frequency of about 800 kHz and an amplitude of about 1 Vpp.
• Increase the frequency until the amplitude of the sinusoid at the top of capacitor C1 is minimum. Write down the (resonant) frequency f0 at which this happens and write down the amplitude (in volts peak-to-peak) of the sinusoid at the top of capacitor C1.
• Make use of the fact that f0=1/(2*pi*sqrt(L*C)) and that at f0 Zeq = R2. Hint: Use voltage division to determine the value of R2.

Determine the "unknown" values for R2 and L1 in Multisim. Show you computations in the lab report. In lab experiment E2 you will have to determine the truly unknown values of R2 and L1 of a real inductor.

P3. Tuned RF Amplifier. Ideally, the RF amplifier amplifies the frequencies of all radio stations. Thus, in the absence of any method to filter out a desired radio station, all stations are received simultaneously and played through the audio amplifier. The circuit shown below uses a parallel resonant circuit consisting of L1, C5 and R5 to filter out a specific radio station. The capacitor is variable so that the resonant circuit can be tuned to the frequency of a particular radio station.

Implement this circuit in Multisim and determine its resonant frequency f0 = 1/(2*pi*sqrt(L*C)). Set the waveform generator to generate a sinusoidal waveform with an amplitude of 50 mVpp and a frequency of 500 kHz. Increase the frequency until the amplitude of the sinusoid on the oscilloscope reaches ist peak value. The frequency for which this happens is the resonant frequency f0. Note the amplitude A of the sinusoid at f0. Then find the frequencies f1 below f0 and f2 above f0 for which the amplitude is A/sqrt(2). The difference f2 - f1 is the bandwidth of the resonant circuit. The frequencies f0, f1, and f2 are shown graphically in the following figure.

The parallel R,L,C circuit implements a bandpass filter. The bandwidth of the filter is determined by the resistance of R (which includes losses in the inductor L and the capacitor C).

#### Lab Experiments

E1. Radio Frequency (RF) Amplifier. Build the RF amplifier that you investigated in problem P1 on your breadboard. The schematic is repeated below for your convenience.

Use the waveform generator to generate a sinusoidal waveform with amplitude of about 50 mVpp as input signal for the attenuator in front of the RF amplifier. Measure the voltage gain at f = 100 kHz, 300 kHz, 500 kHz, and 1 MHz. Compare with the results from the simulation in P1.

E2. Winding and Measuring an Inductor. To make the AM radio tunable, we use a tunable bandpass filter consisting of a parallel resonant circuit with an inductor and a variable capacitor. The capacitor and its wiring (connecting the two sections in parallel) is shown in the pictures below.

The inductor is wound on a ferrite rod (R-037400-61 from CWS ByteMark) and serves two purposes, (i) as an inductor and (ii) as an antenna ("loopstick" antenna). Before winding the inductor, wrap a piece of paper around the ferrite rod and secure it with tape such that the paper can be moved back and forth on the rod.

Note: The ferrite rods are fragile! If you drop them on the floor they will break. They are fairly expensive and I have only a limited supply available, so act accordingly!

To wind the inductor use about 12 feet of #28 enamel coated magnet wire. To start winding the coil, tape one end of the wire to the end of the paper sleeve and the rod as shown below.

Be careful not to kink the wire, it easily breaks or the enamel coating gets damaged and causes short circuits between windings. If the wire breaks, scrape the enamel off of both ends (be careful to scrape it off all around the wire) of the break and solder the wires back together. The coil is wound in two portions. The first portion consists of 50 turns of wire. Then make an intermediate tap by pulling out a loop of wire and twisting it. After that wind another 30 turns in the same direction for the second portion. When you have wound all turns of the second portion, secure the end with tape and cut off any wire in excess of about 4" from the end of the coil. The completed "loopstick" antenna is shown below.

To be able to use the inductor/antenna, you need to scrape off (using a knife and/or sandpaper) the enamel at both ends and at the intermediate tap. Make sure to scrape the enamel off all around the wire, solder will not stick to the enamel and will not make a reliable electrial connection. Solder short pieces of wire from your breadboard kit to the coil connections so that you can use them with the breadboard later on.

When you have completed your inductor, measure the inductance of the 50 turn part and the whole 80 turn part as described in problem P2. The schematic is shown below. Note that the 50 ohm resistor is inside the waveform generator on the testbench.

The resonance frequency of the series R,L,C circuit (when the LC combination acts like a short circuit) should be in the range of about 500 kHz to 1.5 MHz. Determine both the inductance of the coil and the series resistance for the 50 turn and the 80 turn portion of the inductor. Show your measurements and computations in the lab report.

E3. Tuned RF Amplifier. Use the inductor from E2 (the whole 80 turn portion) and the variable capacitor (with the two sections connected in parallel as shown here) at the front end of the RF amplifier on your breadboard as shown in the schematic below.

Turn the capacitor to a position about midway between the two end positions. Use the waveform generator on the lab bench as described in P3 to find the resonant frequency f0 and the cutoff frequencies f1 and f2. Compare to the results you obtained in problem P3.

E4. Completing and Testing the AM Radio Receiver. Now all that needs to be done to complete the AM radio receiver is to put all the pieces together.

Important: Building a radio on a breadboard requires care, good circuit building technique, and often some experimentation. The frequencies involved are moderately high and the capacitance between the columns of the contacts on the breadboard becomes significant. Also, the overall amplification of the radio circuit has to be high so that the microvolts from the antenna are turned into volts at the speaker. There is the potential for feedback from the output stage back to the input stage which manifests itself in the form of loud whistling or motorboating sounds. Feedback occurs through capacitance within the breadboard and also through inductance of the component wires. It is imperative to keep all leads as short as possible. In addition, the metal base of the breadboard needs to be connected to circuit ground so that it acts as a ground plane and reduces the capacitve coupling between different parts of the breadboard.

The picture below shows how to make a ground connection to the metal base of the breadboard. Remove one of the little screws that holds the breadboard in place. Scrape the paint off the metal base around the hole for the screw. Then wind the blank end of a wire around the screw and srew it back in. The other end of the wire gets connected to circuit ground on the breadboard.

Below is the schematic of the AM demodulator and the audio amplifier that you built in the last lab. Capacitor C8 can be added optionally to increase the gain of the audio amplifier (from 20 to 200). The output of the RF amplifier gets connected to the left end of C7 and replaces the AC voltage source V2.

The figure below shows one way to arrange the parts of the AM radio on the breadboard (click on the picture to enlarge it). The AM radio band extends from 540 kHz to 1.6 MHz. For the lower end of the band use the 80 turn portion of the inductor. For the upper end of the band use the 50 turn portion of the inductor.

Here is another view of the arrangement of the parts on the breadboard (click the picture to enlarge).

When testing the radio keep in mind that, when you are inside a building made from concrete, the rebars that are used to reinforce the concrete act like a Faraday cage that passes little if any AM radio waves. Try your receiver near a window or go outside of the building.