Discrete Component Audio-Frequency RC Filters




Web Page Introduction

Building audio filters for home built popcorn receivers using discrete components for the active elements can be both fun and instructive. What components go into a given filter is often determined by which parts are on hand at the time of construction. Presented is a loose collection of filter ideas and whenever possible, the design theory. Practical examples are included which were tested in a basic direct conversion receiver using a diode ring mixer with various AF preamplifiers and an LM386N power amplifier driving headphones.

Basic Resistance-Capacitance Filter Design

Presented in Figure 1 are some basic examples of simple resistance-capacitance filters. Low frequencies are attenuated by a series capacitor and a shunt resistor to ground. Conversely, high frequencies are attenuated by a series resistor with a shunt capacitor to ground. The formula for the 3 dB cutoff frequency which is the frequency in which the reactance of the capacitor equals the resistance component value is shown below along with two derivations.
The normal response of these networks is a 6dB drop in output voltage per octave. A faster drop can be achieved by cascading filters in series as is shown in Figure 1 with the series lowpass filter using 2 networks. Unfortunately, interactions between the two series filter sections will change the cutoff frequency from the design frequency somewhat. Lowpass, highpass, bandpass and band-reject (notch) filters can be made using RC networks although this web page will focus mainly on the lowpass and bandpass types.

Although, many amateurs are now using LC network designs or low-noise operational amps for receiver audio filters, RC filters using discrete components can be low cost and practical alternatives. RC networks enjoy some advantage over LC networks, namely they do not pickup inductive hum and they are frequently less expensive and more compact in size.





Interstage Filters

Discussion

Early transistorized AF amplifier stages were mostly transformer coupled from stage to stage. Eventually, RC-coupling became popular and with the advent of the silicon transistor direct coupling 2 or greater stages became common practice. Direct coupling increases low frequency response and often reduces the parts counts used in AF preamp circuits. RC and direct coupling allows the designer to shape the stage frequency response using resistor and capacitors in numerous different network configurations. This section will focus on interstage filtering RC-coupled amplifiers.



Every amplifier has an optimal frequency range that it will operate over. RC-coupled stages maybe designed to operate over a frequency range that best suits the radio amateur. In Figure 2a , we see can see that the coupling capacitor CC is really in series with the two resistors RC and RL. At midrange to high audio frequencies, the reactance of CC is negligible and there will be very little AC voltage drop over it. If we lower the audio frequency, the capacitive reactance CC will increase by the formula XC = 1 / 6.283 x Frequency x CC. The lower the frequency, the greater the voltage drop across capacitor CC will be. If the frequency is lowered to the point where the the capacitive reactance of CC is equal to the the series resistance of the circuit the AC voltage drop will be 3dB down from the source voltage.
Figure 2b shows the voltage source equivalent of figure 2a. In these diagrams, it is important to note that the value of RL represents the total input impedance of the subsequent transistor stage. For a given RC and RL, the greater the CC value, the greater the low frequency response. This fact is often conversely used by radio amateurs to attenuate 60 cycle hum by using high value capacitors such as 0.1uF for coupling caps.
Emitter bypass caps also can have an effect on the low frequency response of an amplifier. The lower the XC of an emitter bypass cap, the greater the low frequency response. A rule of thumb is to use a bypass capacitor with an XC of 100 or less at the lowest frequency you wish to amplify.

Project

Shown in Figure 3a and 3b are two RC-coupled PNP amplifier stages that form an interstage bandpass filter using shunt and series capacitors. If the 3dB lowpass cutoff frequency is at least ten times the 3dB highpass cutoff filter, the two filters can be considered independent of one another.
The basic design formulas are shown however they do require some clarification.
The 3dB highpass cutoff frequency is the frequency where the reactance of of the coupling capacitor CC equals the series resistance of the input impedance of Q2 plus resistor RL of Q1. While the RL value is straight forward, the input impedance is a more complex affair. Figure 2a shows how Q2 looks in terms of its AC input resistance. The input resistance is composed of R1, R2 and the Q2 emitter resistor. In order to calculate the AC emitter resistance, the DC emitter Current (Ie) must be first calculated using a calculator or computer program. Get a transistor textbook if you do not know how to do this or just assume 1 mA for Ie. To calculate the AC emitter resistance r'e in ohms, divide Ie into 26.
The formulas are shown in Figure 3a. The base resistance is calculated by multiplying the transistor Beta by the sum of r'e plus RE which is the resistance value of the component resistors hooked to the Q2 emitter. If the emitter is bypassed, make RE zero, if emitter degeneration is used, the resistance value RE will be the resistance of the unbypassed resistor. To solve for the AC input resistance, use the parallel circuit formula for R1, R2 and R input.

The 3dB lowpass cutoff frequency is is the frequency in which the reactance of the shunt capacitor CS is equal to the resistance of RL in parallel with the input resistance of Q2 (R input calculated as above).
Figure 3b shows a practical interstage filter with a low and highpass cutoff near the desired 10 times differential. Of interest, is the emitter degeneration on Q2. This is done to raise the AC input resistance of Q2, stabalize the amp, reduce distortion and to aid in setting the filter capacitor values. The calculated values are shown to the right of the figure 3b schematic.

A PSPICE run of the 3b interstage filter can be found on this AF Filter Supplemental Page




The Flicker Receiver

Below in Figure 4 is a minimal parts direct conversion receiver that I built using the above interstage filter concept. This project was inspired by Wes Hayward's MicroMountaineer project from QST for 1973 and Solid State Design. It is both a great challenge and thrill to build and operate minimalistic rigs. All that is required for this receiver is a front-end bandpass filter. The double-tuned filter portrayed in the 30M Receiver Project was used in my version. The diode ring mixer was a TUF-1 by Mini-Circuits as it is smaller than the SBL-1. The capacitor value used for CS was 0.1uF which sets the 3dB lowpass cutoff frequency at around 638 Hz. This might seem low, but since there is only one lowpass filtering network, I prefer to go low and start rolling the highs off as quickly as possible. If you do not have the 0.22uF CC capacitor, you can use a two 0.1 uF caps in parallel which gives a calculated 3dB highpass cutoff of ~80 Hertz. Obviously the 10 times low-to-high pass filter seperation rule was somewhat ignored in this receiver design, but it seems to work alright. In addition, do not expect dramatic lowpass filtering from just one RC network. It is interesting that the CS capacitor substantially reduced broadcast interference problems in the receiver when it was first tested ungrounded and then after soldered to ground.
The 3 stage preamplifiers have considerable gain and drive the final and headphones with good volume. At full volume, AF feedback may erupt if leads and connecting wires are excessively long. Although my version does not have hum problems, one possible improvement would be to add the active decoupler to the first stage. It is found in every other receiver on this web site and would minimize any chance of 60 Hertz hum getting into the Q1 stage. This little receiver does a good job for so few parts and can be built extremely compactly.





A video capture of the prototype Flicker circuit board laying on the Flicker schematic is shown immediately below. Note that room on the ground plane was left for further experimentation. The object to the right is the LM386N upside down with pins 2 and 4 soldered to the copper circuit board.
Below the prototype board is an actual receiver with an antenna lowpass filter installed in a Hammond 4 X 3 inch die-cast case as part of a personal version of W7ZOI's MicroMountaineer transceiver. The loose red and black wires are temporary B+ and antenna cables used in testing the receiver. The crystal oscillator, sidetone and transmitter stages have not yet been installed. The transmitter puts out 1 watt onto the 30 Meter band and features solid state T/R switching. This is one of my all time favorite projects and has provided many hours of fun and even some DX.





It is important to note that the formulas given for interstage RC filter data are simplistic and do not account for other factors such as parasitic, Miller effect and wiring capacitance and the frequency to gain dependence of the active device. The results however will be ballpark and provide a practical approach for your designs.
I have built a few successful active filters using nJFETs in both common drain and as source followers. With these transistors, the low frequency calculations are similar to those of BJTs. To use the Figure 3a formula for the highpass 3dB cutoff frequency, R input would be the gate resistance and RL the source resistance of the previous stage. For the high frequency calculations, things get more complex and the effects of the circuit and component capacitance come into play. The lowpass formula maybe used but the CS value will be a bit low in most cases. The actual 3dB cutoff value maybe somewhat different than the design value. Experimentation will lead you to good fun and enhanced knowledge of electronics.


Fourth Order Peaked Lowpass Audio Filter

Peaked Lowpass Filter

Shown in Figure 4, is an excellent lowpass filter designed by Wes Hayward, W7ZOI and was presented in the now defunct HAM RADIO magazine for April 1974. For the original article, Wes built a ten pole filter however, a four pole version is shown in Figure 4. I built a filter having eight poles and was very impressed with its performance during testing on 40 meters with crowded band conditions. At the input is a single pole section used to properly bias the succeeding stages and to provide a high pass response, attenuating low frequencies and 60 - 120 Hertz hum. Following the input stage are pairs of NPN and PNP transistors which form a 2 pole filter pair that make a unity gain, non-inverting amp with very high input impedance due to the wrap-around feedback. The feedback from the collector of the PNP transistor back to the emitter of the NPN transistor takes the very high gain of the two stages and forces it back to a voltage gain of 1.
The Q of each filter pair is 1.9 giving a 6dB bandwidth of 200 Hertz. The center frequency is 540 Hertz and attenuation of the ten pole filter is 75dB at 1200 Hertz. The net gain of the ten pole filter is 28 dB. Transistor choices include 2N3904 or lower noise equivalents for the NPN transistors and 2N3906 or lower noise equivalents for the PNP BJTs. example: 2N3565, 2N5089, 2N5087, 2N3638 etc. Allowable component tolerances are 10 - 20 % with minimal degradation of performance.
A PSPICE run of the 4 pole filter shown can be found on this AF Filter Supplemental Page

Solid State Design for the Radio Amateur contains additional useful information on building discrete component audio filters. For fun, I connected the 4 pole filter to a modified Flicker receiver prototype and was suitably impressed.




Miscellaneous Filters

Single common emitter audio filter/amplifier stages maybe used in popcorn receivers. Below is a collection of four such amplifiers. Figure A has a 300 hertz bandwidth with a center frequency of 800 hertz. Voltage gain is 1. Figure B has a low pass response with a breakaway frequency of 3 KHz. Figure C has a bandpass response center frequency of 1 KHz and is Figures B and D cascaded. Figure D has a highpass response with a cutoff frequency of 360 Hz. Figure B, B and D have a no load voltage gain of ~20. All filters can be built using the ubiquitous 2N3904 or equivalent NPN BJT. The cutoff frequencies maybe changed up tp three decades by changing the capacitor values by a common factor. Trial and error or SPICE simulation are practical approaches as no design equations are available.




A Electronics Workbench simulation of the 6A amp can be found on the AF Filter Supplemental Page




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