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Output Impedance Matching with Fully Differential Operational Amplifiers

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Output Impedance Matching with Fully Differential Operational Amplifiers Texas Instruments Incorporated Amplifiers: Op Amps Output impedance matching with fully differential operational amplifiers By Jim Karki Member, Technical Staff, High-Performance Analog Introduction synthetic imped ance matching is more complex. So we Impedance matching is widely used in the transmission of will first look at the output impedance using only series signals in many end applications across the industrial, matching resistors, and then use that as a starting point to communications, video, medical, test, measurement, and consider the more complex synthetic impedance matching. military markets. Impedance matching is important to The fundamentals of FDA operation are presented in reduce reflections and preserve signal integrity. Proper Reference 1. Since the principles and terminology present- termination results in greater signal integrity with higher ed there will be used throughout this article, please see throughput of data and fewer errors. Different methods Reference 1 for definitions and derivations. have been employed; the most commonly used are source Standard output impedance termination, load termination, and double termination. An FDA works using negative feedback around the main Double termination is generally recognized as the best method to reduce reflections, while source and load termi- loop of the amplifier, which tends to drive the impedance nation have advantages in increased signal swing. With at the output terminals, VO– and VO+, to zero, depending source and load termination, either the source or the load on the loop gain. An FDA with equal-value resistors in (not both) is terminated with the characteristic imped- each output to provide differential output termination is ance of the transmission line. With double termination, shown in Figure 1. As long as the loop gain is very high, the both are terminated with this characteristic impedance. output impedance, ZOUT, in this circuit is approximately No matter what impedance-matching method the designer equal to 2 × RO. chooses, the termination impedance to implement must be Parameter definitions for Figure 1 are as follows: accurately calculated. • R and R are the gain-setting resistors for the amplifier. Fully differential operational amplifiers (FDAs) can pro- F G • R is the impedance of the load, which should be vide a broadband, DC-coupled amplifier for balanced differ- L balanced and, for double termination, equal to Z . ential signals. They also have a unique ability to convert Line broadband, DC-coupled single-ended signals into balanced • RO is the output resistor. differential signals. • VO± is the output terminal. A common method to provide output impedance match- • VOCM is the output common mode of the FDA. ing is to place resistors equal to the desired impedance in • V is the differential output signal. series with the amplifier’s output. With double termination, OUT± this has the drawback that the signal level delivered to the • VS± is the power supply to the amplifier. line is reduced by –6 dB (or half) from the signal at the • ZLine is the characteristic impedance of the balanced amplifier’s output. transmission line from the amplifier to the load. Synthetic impedance matching allows lower- Figure 1. FDA with differential resistors for output termination value resistors to be used in conjunction with posi- tive feedback around the RG R F ZOUT Output amplifier. The benefit of VIN+ doing this is that the out- Resistor V put attenuation is reduced. S+ This increases efficiency V RO V – O – OUT– by lowering the loss and + Gain-Setting FDA ZLine RL allows support of higher- Resistors + amplitude signals on the – VO+ R VOUT+ line than can be achieved O V VOCM with standard termination. S– Balanced Output Using standard series V Transmission IN– Resistor Line matching resistors to ana- R R lyze the output impedance G F of FDAs is very easy, but 29 Analog Applications Journal 1Q 2009 www.ti.com/aaj High-Performance Analog Products Amplifiers: Op Amps Texas Instruments Incorporated For analysis, it is convenient to assume that the FDA is Figure 2. FDA circuit for analysis of balanced an ideal amplifier with no offset and has infinite gain. Each output impedance output of the amplifier can be viewed as a voltage source with an output impedance of rO. With high loop gain, both rO and the differential output impedance, Z, of the FDA ZOUT will be very small; for instance, the output impedance of Z0 the Texas Instruments (TI) THS4509 is less than 1 Ω at RO VOUT– frequencies below 40 MHz. For output-impedance analysis, r the inputs are grounded so that V = 0 V, resulting in o IN± V V = V . Since we are interested in only the AC O– O± OCM V = V response, and since V is a DC voltage, V is set to 0 V. V O± IN± OCM O± OCM (R /R ) The differential output impedance can be determined from FG VO+ Figure 2: ZOUT = 2(rO + RO); and, since as rO is nearly 0 Ω, ro RO ZOUT ≈ 2 × RO. VOUT+ For an example of how to select the value of RO, let’s look at driving a twisted pair differentially from the FDA. A value of ZLine = 100 Ω is common for twisted-pair cables. For double termination, the source needs to provide RO = 50 Ω on each side for a 100-Ω differential output imped- ance, and the line needs to be terminated with RL = 100 Ω. It is assumed that the output impedance of the FDA is approximately 0 Ω, so 49.9-Ω resistors are placed in each Synthesized output impedance series with each output. In Figure 3, the positive-feedback resistors, RP, are added In a terminated system, it is common practice to take from VOUT+ to VP and from VOUT– to VN. Given a balanced the gain of the amplifier stage from the source to the load, differential system, these resistors provide positive feed- or from VIN± to VOUT±; so gain is given by back around the amplifier that makes R′O look larger from the line than the actual value, R . The amount of positive VIN± RL RF O = × . (1) feedback used determines the scaling and has an effect on V RR+ 2 R OUT± LOG the forward gain of the amplifier. Assuming that the output impedance matches the load impedance, V 1 R Figure 3. FDA differential output impedance with synthesized resistors IN± =×F . (2) VOUT± 2 RG Positive- Feedback It is recommended that RF be RP ZOUT kept to a range of values for the Resistor best performance. Too large a RF resistance will add excessive Output noise and will possibly interact Resistor with parasitic board capacitance VS+ to reduce the bandwidth of the R VP G V RO V – O – OUT– amplifier; and too low a resist- VIN+ + ance will load the output, caus- FDA ZLine RL ing increased distortion. For V – + IN– V V R O+ R OUT+ example, the THS4509 performs G VN O best with R in the range of 300 VOCM F VS– to 500 Ω. In the design process, Balanced Output Transmission the designer first selects the Resistor Line RF value of RF, then calculates RO and RG to match the desired R Positive- gain. The value of ZOUT is then P Feedback calculated as 2 × RO. Resistor 30 High-Performance Analog Products www.ti.com/aaj 1Q 2009 Analog Applications Journal Texas Instruments Incorporated Amplifiers: Op Amps It is convenient to first look at half of this circuit (see Figure 4) to analyze the response of the amplifier to a Figure 5. Simplified view for analysis of impedance seen from the line signal that was applied from the line because resistors RP were added. To determine the output impedance of the amplifier as seen from the transmission line, a signal is ZOUT injected at VOUT– with the input at VIN+ grounded. The RO signal from the other side of the line at V is seen as an IO– OUT+ VO– input signal to the amplifier, with gain to VO– set by RF/RP. V R Note that the output pins will have a common-mode volt- P P V age set by V , which is assumed to be a DC voltage and Virtual OUT+ OCM R is set to 0 V for AC analysis as before. Short P VOUT– In a balanced system it is assumed that the differential V N R signals are symmetrical and 180° out of phase. Therefore O V V = –V , and O+ OUT+ OUT– IO+ RF RF VVOO−+=− UT ×=VOUT− × . RP RP Figure 4. Simplified view for analysis of The positive feedback from adding resistors R affects adding RP P the forward gain of the amplifier and adds another load in parallel with R . Accounting for this effect and the voltage R R L P F divider between R′ and R ||2R , the gain from V to VOUT+ O L P IN± VOUT± is given by RG RO VOUT± RF 1 VO– . (4) + V =× – OUT– VIN± RRGO22′ + RRLP|| RF V FDA − P + RRLP|| 2 RP – The derivation of this equation is left to the interested reader. Design is best accomplished by first choosing the values Thus RP effectively adds positive feedback to the system, of RF and R′O. Next, the required value of RP is calculated resulting in an in-phase response at VO– to a signal from to arrive at the desired ZOUT. Then RG is calculated for the the line. This in turn makes R′O appear (from the line) to required gain. These equations are easy to solve when set be a larger-value resistor than it actually is. Inclusion of up in a spreadsheet. To see an example Excel® worksheet, the other half of the amplifier permits the differential click on the Attachments tab or icon on the left side of the response of the circuit to be shown as Adobe® Reader® window.
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