RF Workbench Page 1
This web page is the first installment of a 2 part series that explores basic measurement of RF circuits.
Part 1 examines practical oscilloscope-based voltage measurement and power calculation. Power calculation requires basic math, however, using software is an option for those who truly dislike crunching numbers. I borrow heavily from the work of Wes, W7ZOI per correspondence and from EMRFD
Ignite your bench measurements! Better measurement fidelity can inspire confidence, creativity, accuracy and fun.
Measuring the Peak-to-Peak Voltage of a Sine Wave
To calculate the power of a circuit, you must first measure the AC voltage. Assuming your scope is calibrated, the first step is to measure the amount of vertical deflection on the screen.
In the figure to the left, the vertical deflection is 4.1 cm. Multiply this measurement by the volts/cm setting of your scope. Lets assume your scope was set to 0.1 volts/cm. Thus the result is 0.41 volts. One final multiplication is required; you must multiply the resultant voltage by the attenuation ratio of the probe. In most cases, a 10X probe is used. Therefore, the measured peak-to-peak voltage is 0.41 x 10 = 4.1 volts.
This signal has a major problem; it is distorted. To calculate the power from peak to peak voltage, one requires a sine wave. To obtain a sine wave, the distorted signal must be low-pass filtered. Consider the scope tracings which follow:
On the left hand side of the figure is waveform with harmonic distortion. On the right hand side, the same VFO output was filtered by a 5 element Chebyshev low-pass filter before measurement. The displayed power for each was calculated from the peak-to-peak voltage. Compare the waveforms and calculated powers of the 2 outputs. Only the sinusoidal power is accurate. The mathematical formula to assess power is discussed in the next section.
Shown in the figure above is the distorted and the low-pass filtered output of an 8 MHz VFO. Power in dBm was calculated from the peak-peak voltages labeled as Vpp. Most builders with a cathode ray oscilloscope (CRO) will quantify power from the measured peak-peak voltage. Note that the Rigol scope used in these experiments also displays the RMS value. If you have a digital storage oscilloscope (DSO), power can be calculated from the displayed RMS value.
Refer to the figure above. The same 8 MHz VFO is examined with a 50 ohm terminated oscilloscope. The 50 ohm measurement technique has greater sensitivity and will be discussed later on this web page. In all 4 cases shown, the vertical scale is 0.2 volts/cm. The output of the VFO is low-level to allow safe examination in a spectrum analyzer.
Spectral analysis of the distorted 8 MHz signal. The second harmonic (16 MHz) is about 22 dB down from the fundamental. The signal is rich in harmonic junk which causes error in the calculation of the output power. Each vertical square is 10 dB. Each horizontal square = 20 MHz. The harmonics go 2x fundamental, 3x fundamental, 4x fundamental and so on.
Spectral analysis of the 8 MHz VFO after passing through an N = 5 low-pass filter. The second harmonic is now about 40 dB down and the 3rd harmonic is almost down in the noise. Each horizontal square = 10 MHz.
The breadboard of the 8 MHz oscillator oscillator used in the above experiments. The output drove a BJT amp biased to give distortion and a 50 ohms output. The frequency was adjusted by a very high Q air variable trimmer capacitor seen to the left.
Low-pass Filter
Some builders may have wondered why clean, sinusoidal signal generators are often featured on this web site. To calculate power, no low-pass filtering is required. Now you know why. If you have a distorted signal, a stiff low pass filter is required. Wes, W7ZOI suggested to try using N = 5 Chebyshev low-pass filters with 0.2 dB of ripple at about 1.2x the signal frequency. Designing low-pass filters is beyond the ability of many homebrewers, so using pre-designed filters from a filter table is a good option for these builders. Consistent with this, the filter used in these experiments was selected from a print copy of the ARRL Handbook for Radio Amateurs and is shown below.
The calculated inductor values were as follows: 0.68 uH = 15 turns on a T37-6 powdered iron toroid. 1.42 uH = 21 turns of a T37-6 core. Windings were removed and/or squished or expanded slightly to get the exact desired values while connected to an accurate inductance meter.
Calculating Power (dBm and mW) from Peak-to-Peak Voltage
To calculate the power from peak-peak voltage, the load impedance (Z) must be known. In RF design, the standardized impedance value is 50 ohms, For CATV and video, 75 ohms is common and in audio and telecommunication design, a 600 ohms impedance is often used. Although technically any Z can be used, we will conform to the 50 ohms RF impedance standard on this web page.
The SI unit of power is the watt. In radio, we might see the term dB used. However, dB is a decibel comparison between 2 signals and not an absolute value like the watt. A common and very useful term is dBm. dBm is the measured power ratio in decibels referenced to 1 milliwatt. dBm measures are an absolute power and very useful because both large and small signals are quantified with 1 number. Here are some bullets to contemplate:
0 dBm = 1 mW- 3 dB is = ~2mW; so doubling the power from 0 dBm
equals a 3 dB increase
in power
- Increasing the power from 0 dBm to 10 dBm is a 10 dB increase in
power. The power is now 10X baseline or 10 mW
- 20 dBm = 100 mW
- -27 dBm means
that the output is ~500 times less power than 1 milliwatt. -27 dBm =
0.002 mW or 2 microwatts
Hopefully over time, you will ingrain the concept of logarithmic power gain or loss (dB) and power referenced to 1 mW (dBm). A very useful tutorial from Wes, W7ZOI is linked here. This is bread and butter radio design information.
The chart above really helps one to visualize the relationships of mW, AC voltages and dBm
In order to get from peak-to-peak voltage into power, math is required. A simple formula is shown above. You may elect to skip the math and just use software to calculate dBm or mW from peak-to-peak voltage. There are a number of programs available; one of which is here as Applet F. As previously mentioned; for this web page, the impedance is always 50 ohms.
If you lack a scientific calculator, Google has math functions. Shown above is a logarithm calculation
In search of 50 ohms
How do I to tell whether or not an amplifier circuit has a 50 ohms output impedance? I get this question often.
From my experience, a 50 ohms output impedance must be created by using a 50 ohm resistance somewhere in the circuit. There are many ways to do this. For example, by placing a 50 ohm collector resistance in a BJT amplifier, a 50 ohm drain resistance in a JFET amplifier, or by placing a fixed resistance in parallel with a collector/drain transformer and using a secondary winding to get an output impedance of 50 ohms. Additionally 50 ohms output impedance may be forced by using a 50 ohms series resistance or in some cases, a 50 ohms attenuator pad on the output of a low impedance stage.
The following diagram, explores 1 method to get a 50 ohm output impedance in a basic amplifier. It does not matter if the transistor is a JFET or a BJT, the principle is the same. This diagram and tutorial are simplistic and meant to help novice builders learn to design their own amplifier stages. It should be mentioned that any resistance can be connected across the output of a stage to calculate power, however, this web page just considers 50 ohms.
The above figure specifically describes a broadband or untuned amplifier. A FT37-43 ferrite toroid was used as this is a common part. Other ferrite toroids can be substituted, however, be aware that any specified amplifier gain may vary, as well as the chart depicting the minimum number of turns will not be applicable.
Consider the BJT amp shown. The transformer primary winding is shunted with a parallel 1800 ohm resistor. This establishes a collector impedance of 1800 ohms. The resistor also lowers the Q of the inductor somewhat which may help reduce parasitic oscillations. The 1K8 resistor "forces" a 1K8 ohm collector output resistance in the primary winding. To transform this impedance to 50 ohms a secondary link is used; in this case 3 turns. The primary to secondary turns ratio is calculated. 1800 ohms divided by 50 ohms = 36. The impedance ratio is therefore 36:1. The turns ratio is the square root of the impedance ratio. Thus the turns ratio is 6:1. The primary winding must have 6X the number of turns of the secondary winding.
Why just not wind 6 turns for the primary winding and 1 turn for the secondary winding might be a question a new builder would ask? The answer is that the smaller or secondary winding should have have an inductive reactance (XL) of 4X the impedance it is connected to. Thus for a 50 ohm circuit, the XL should be at least 200 ohms at the design frequency. This is a design rule which is often broken. It only serves as a design guide. The 4X rule is used because if the XL of the secondary winding is lower than 4X the impedance, the amplifier may have unwanted signal losses and impedance matching problems. The chart to the right of the amplifier shows the minimal numbers of turns on the secondary for a few common frequencies using an FT37-43.
Thus for our 7 MHz amplifier, the minimal number of secondary windings is multiplied by 6 (the turns ratio) to give the 18:3 turns ration shown. For ferrites other than the FT37-43, you can easily calculate the minimum number of turns using the inductive reactance formula and the turns versus AL data for a given ferrite toroid.
For AC measurement purposes, a 50 ohm purely resistive load should be temporarily connected between the output link and ground. This might be a 51 ohm resistor, a 49.9 ohm 1% metal film resistor, 2 parallel 100 ohm resistors, or some other "50 ohm" load. Peak-to-peak voltage is measured across the load and then the power in dBm or mW may be calculated. After measurement, the 50 ohm load is removed and the circuit connected to the succeeding stage.
51 and 49.9 ohm resistors
Case Study
Pretend that you breadboarded the above circuit entitled "Case Study". This is a 50 MHz crystal oscillator and buffer. The crystal fundamental frequency is 16.7 MHz, but the L1 tank is tuned to its 3rd overtone; 50.0 MHz. You measure and record the peak-to-peak voltages at the points labeled A, B and C.
The peak-to-peak voltages are shown as Vpp. The vertical scale (volts/cm) is shown on the bottom of each figure.
Examine point A. The AC voltage is 12.1 volts peak-peak. Compare this to the peak-peak voltage at point B. Note the difference. Some builders have sent me emails after observing similar differences in AC voltages on the primary and secondary transformer windings in their circuits. These builders felt something must be wrong?. This is normal. You can expect the peak to peak voltage to roughly decrease (or increase) by the transformer turns ratio. For our example above this means the 12.1 volts peak-peak to decrease by a factor of 4.3 (13 / 3 turns ratio) which is 2.8 volts peak-peak. In our case, the measured secondary peak-peak voltage was 3.08 volts - in the ballpark. Please remember that this is a very coarse guide only. It helps you to know what to reasonably expect during signal viewing.
The peak-to-peak voltage change in accordance with the transformer turns ratio is simplistic and describes the "ideal transformer". To understand real world transformer function, one must contemplate factors such as Ohm's law for AC, conservation of energy (this is what causes the voltage to drop while preserving power) and basic transformer behavior. These basic principles are explained in publications such as The ARRL Handbook for Radio Communications or the RSGB Radio Communication Handbook. An old high school physics text book might even be a better reference.
Here are the case questions:
- 1. Calculate the power in dBm at point B
- 2. Calculate the power in dBm at point C
- 3.What is the attenuation in dB of the 50 ohms attenuation pad?
- 4. What is the output power in mW of this stage?
Click on this link for the answers and see the actual resistor values of the attenuation pad.
Note that the 50 ohms pad connected to the Q2 output link is what forces the output impedance to 50 ohms. This is a useful technique and is commonly used in feedback amplifiers to help establish the output and input impedances. Is this cool or what?
Finally it is worth mentioning that placing a 10X probe at point A will de-tune the L-C tank circuit somewhat and thus alter the AC voltage. In real-world building; to tune an amplifier such as Q2, tweak the variable capacitor (CV) with your 10X probe connected to point C.
The breadboard of the 50 MHz oscillator prototype.
Oscilloscope Probing
10X Oscilloscope Probe
Please refer to EMRFD Chapter 7 for invaluable information concerning measuring power in RF circuits. The 10X oscilloscope probe is one of the most important measurement tools to have on your bench. There are countless web articles concerning the 10X probe, therefore, they will not be discussed in detail. For HF work, they are pretty much essential.
The 10X probe attenuates the signal by a factor of ten. This has to be taken into account. Some oscilloscopes including most DSOs automatically account for this after you select your probe attenuation in a menu. You select 10X probe for a given channel and this is stored in memory. It is also important to properly adjust the compensation capacitor on the 10X probe. Consult your owners manual to do this.
When do you use a 10X probe ? was a question I asked for many years The 10X probe is used for in-situ ("in place", or "in circuit" ) voltage measurement and in situations where you can afford a 10X reduction in sensitivity. In low level measurements such as millivolt level measurements, the reduced sensitivity of a 10X probe may reduce or disallow accurate measurement. Additionally, the ~20 pF capacitance of a 10X probe can detune a circuit; this is especially true at VHF on up.
Close up of the Rigol oscilloscope probe 10X and 1X switch.
50 ohm Terminated Oscilloscope
At RF, we generally work with (or try to work with) circuits with 50 ohm impedances. It is possible to perform your measurements in a purely 50 ohm environment. Instead of using a 10X probe, the oscilloscope input is shunted to ground with a 50 ohm resistor and the circuit under test is connected to the scope with 50 ohm impedance coaxial cable. On my Rigol scope, I have Channel 1 set up for the 10X probe work and Channel 2 set up for a 50 ohm environment.
I asked Wes, W7ZOI about performing measurement in a 50 ohm environment. I learned that the main advantage of the 50 ohm approach is that the impedance is always well known and controlled. The second virtue is the 10 greater voltage sensitivity. The increased sensitivity in low level measurement is really fantastic. In certain cases, small signals which I could not accurately measure with a 10X probe, gave an excellent scope tracing and consistent voltage reading with a 50 ohm measurement technique. Signal viewing may also be enhanced. For example, in a few cases, I have observed harmonic distortion with a 50 ohm terminated scope unseen with a 10X probe The distortion was confirmed with a spectrum analyzer.
If you have never performed measurement in a 50 ohm environment, consider trying it out - you will enjoy it. Commercial 50 ohm feed-through devices which connect to your oscilloscope are available. You can easily homebrew your own. Try to keep the 50 ohm termination as close to the oscilloscope input as possible.
Establishing a 50 ohm impedance measuring environment. The oscilloscope input is terminated with a 50 ohms resistance and connected to a device with a 50 ohms output impedance via 50 ohm coaxial cable.
A homebrew 50 ohms scope terminator module. This module is connected to the oscilloscope input via a 9 cm 50 ohms impedance coaxial cable. RG-174 was used to wire up this particular device. Two parallel 100 ohm resistors form the 50 ohm load.
The homebrew module shown above is not an ideal 50 terminator, however, no female BNC connectors were available at the time of construction. The ideal homebrew solution is likely to place a male and female BNC connector in a small metal box very close to one other so that very short interconnecting wire could be used. The box would hang off of the oscilloscope. Better still are commercial 50 ohm feed through terminators which thread right onto the oscilloscope BNC input jack.
Shown above — a commercial 50 ohm feed-through BNC terminator on my oscilloscope input.
RF Current Sampler
Figure 1 is a basic circuit to sample RF current from a power stage such as a QRP transmitter. Many experimenters lack 50 ohm step attenuators which are rated to handle transmitter-level power. One basic solution is to sample the RF current of the power amplifier using a wideband step-down transformer. The RF current sample port is terminated in a 50 ohms impedance device. This may include a spectrum analyzer, power meter, receiver with an attenuator, or a 50 ohm terminated oscilloscope. A good example is to examine a a transmitter's spectral purity with a spectrum analyzer. The output power at the sample port is around 20-22 dB down. A 50 ohms impedance step attenuator can be used to further reduce the power level to whatever is desired. For this chore, a typical experimenter's 1-2 watt step attenuator can be used as it never "sees" the higher wattage transmitter power.
For example, a 5 watt amplifier 20 dB down is 0.05 watts or 50 mW at the RF current sampler port. 50 mW = 17 dBm. To examine this signal with a spectrum analyzer you may wish to decrease the power down to -27 dBm. The chart which follows illustrates the whole process.
A Hammond chassis shields the RF current sampler used on my bench.
The above graphic illustrates 2 methods to examine the output of a transmitter in a spectrum analyzer. Method B is described in this section. The dummy load must be able to handle the transmitter output power, however a 5 or 10 watt dummy load is easy to make (This is a QRP website). Method A requires a step-attenuator which can handle the transmitter output power. The low-level power meter promotes the need to quantify the output power before you connect anything to the output of the attenuator. This is also true for Method B.
Always measure the output power at the RF sample port with your oscilloscope or low-level power meter before hooking up any expensive low-level measurement device such as a spectrum analyzer.
Miscellaneous Photos
