The Cause and Eliminate Method of Self-excited Oscillation in Long Cable Amplifier Circuits

SMA long cable distributed capacitance is easy to trigger broadband amplifier circuit’s selfoscillation. In this study we design an amplifier circuit based on OPA691 chip, discuss the influence of long cable’s distributed capacitance, then prompt a solution to add 50Ω compensation resistor between the output terminal and the load capacitance. According to the Tina simulation analysis, when 50Ω compensation resistor is added, bode diagrams show amplitude characteristic is smaller than 0 dB at -180 ° phase. The selfoscillation also disappeared in actual circuit measurement, which verify the rationality of this solution.

Figure1: Principle of self-excited oscillation [1] From which can deduced the gain A  of the amplifier circuit with negative feedback as follows: The self-excited phenomenon must meet the selfoscillation conditions, feedback loop coefficient :  Ḟ̇= -1.
The conditions consist of two parts: a. Amplitude condition is: Where   is the phase of the amplifier  ̇,   is the phase of the feedback network  ̇,   +  is the phase difference between the feedback signal and the input signal.When actual circuit meets the phase condition and positive feedback, also satisfy ](n=0,1,2• • • ), the circuit is in an unstable state, which may also produce self-oscillation [2] .
The physical meaning of the above description is: If normalized vector signals which enter the broadband amplifier at one moment into a signal unit, then the broadband amplifier will output the corresponding vector of 1 × ̇ units; and then through the feedback network  ̇ back to the broadband amplifier, will returne corresponding vector of 1× × ̇ units; if 1× × ̇=1, it means that without external input signals, the feedback signal can maintained in the reciprocal transfer feedback path, keeping the same energy [3] .This means that the system can output equal amplitude oscillations without input -that is, self-excited oscillation.

SMA LONG CABLE DISTRIBUTED CAPACITANCE'S IMPACT ON OPERATIONAL AMPLIFIER
SMA coaxial cable's center coaxial conductor and outer shield metal can be equivalent to the distributed capacitance as shown in Fig. 2.Refer to the manufacturer's information, we use SMA distributed capacitance about 96.1 pf/m.So introduce the SMA cable equivalent of increasing the capacitive load of broadband amplifier circuit, and impact the stability of the entire amplifier system [3] . .Refer the OPA691 manual comprehensive analysis Fig. 2 circuit  Ḟ ̇can be obtained in this ideal circuit should be stable, will not occur self-oscillation.This is also demonstrated by circuit simulation using the TINA simulation software provided by TI's official website, as it shows in Fig. 3.However, after considering the influence of the distributed capacitance, the circuit is unstable and may occur selfoscillation in Fig. 4.

SIMULATION OF AMPLITUDE-FREQUENCY CHARACTERISTIC WITHOUT CAPACITIVE LOAD
In the case of uncharged load, analogy the capacitance model of Fig. 2 can simulated the circuit shown in Fig. 3 left, the pote characteristic is shown in Fig. 3  In the self-excited oscillation conditions, when | Ḟ̇| <1, the output signal is continuously reduced, and will not occur self-oscillation.In the frequency of -180 ° phase, the amplitude characteristic is -5.94dB <0dB, the system is stable, will not occur self-oscillation.[Note: set Rf OPA691 bandwidth within 260MHz, beyond this frequency will not occur self-oscillation, the specific derivation refer to OPA691 official website datasheet description [4] .]

SIMULATION OF AMPLITUDE-FREQUENCY CHARACTERISTICS WITH CAPACITIVE LOAD
The following circuit adds the equivalent capacitance to the SMA connected position [5] .The 2m cable introduces about 200pf equivalent capacitance.The effect is shown in Fig. 4.

Figure4: Circuit and baot diagram with capacitive load
From the amplitude-frequency characteristic curve shows that the phase at -180 °, there is 142.04MHz frequency amplitude characteristics 8.46dB> 0dB, to meet the conditions of self-oscillation occurred.Therefore, in the case of 150pF capacitive load, instability will produce self-oscillation.
Through the above comparison simulation is obvious, capacitive load C 7 affect the system's amplitude-frequency characteristics, undermine the stability of the system.

ANALYZE THE THEORY 4.1 CREATE A CIRCUIT MODEL
To analyze the principle of the capacitance, the equivalent circuit of the amplifier circuit in Fig. 4 must be analyzed.Because in fact the amplifier open-loop output resistance is not 0Ω, so the first broadband amplifier OPA691 equivalent to for the flow control voltage source with a amplification factor is  ̇ , the external output contains a resistance Ro, the official manual indicate Ro ≈ 15Ω, as shown in Figure 5.  Figure9: Compensation circuit model From the amplitude-frequency characteristic curve shows, there is 1.25GHz frequency amplitude characteristics -12.55dB <0dB at -180 °phase, and set RF below 260Mhz, there is no frequency instability and positive feedback phenomenon.It proves this method can successfully elimination the self-oscillation.

CIRCUIT MEASUREMENT
The test circuit shown in Fig. 10, in the actual measurement, Vf2 grounded through 50Ω resistor, Vf1 through the SMA cable connected to the oscilloscope which input probe impedance> 1MΩ.Results of testing: Conntect different lengths of cable, the capacitance parameters will change, test results shown in Table 1.According to the summary table, it can be clearly concluded that adding a capacitive load causes the amplifier system self-oscillating oscillation.By introducing a 50Ω series resistor between the output of the op amp and the load capacitor, the self-oscillating oscillation can be eliminated.

Fig. 1
Fig.1shows a schematic diagram of a feedback amplifier. ̇is the amplification factor of basic amplifier ,  ̇ is the feedback coefficient of the feedback network.

Figure2:
Figure2: Distributed capacitance equivalent model In 1.5m line simulation, the distribution of capacitance value is similar to 96.1pf / m * 1.5m ≈ 150pf;the broadband amplifier circuit using TI's OPA691 chip (set the Rf bandwidth to 260MHz or less) to build 8 times the magnification of the in-phase amplification circuit.OPA691 open-loop gain characteristics determine the amplitude characteristic of  :  ̇= 1 1+2

Figure5:
Figure5: Amplifier equivalent circuitOpen-loop simulate the OPA691 circuit , using 1GH inductance L 1 to rcuitdisconnect the AC loop, and through the 1GF introduce C 8 the AC ground attach to the inverting

TABLE 1 :
Measurement results